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url: https://de-wikisource-org.translate.goog/wiki/Translatorische_Bewegung_des_Licht%C3%A4thers?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US
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<title>Translational movement of the light ether - Wikisource</title>
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</div><button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name=pinnable-header.vector-main-menu.pin><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Move to sidebar</font></font></button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button sf-hidden" data-event-name=pinnable-header.vector-main-menu.unpin>Hide</button>
|
|||
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</div>
|
|||
|
|
<div id=p-navigation class="vector-menu mw-portlet mw-portlet-navigation">
|
|||
|
|
<div class="vector-menu-heading sf-hidden">Navigation</div>
|
|||
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<div class=vector-menu-content>
|
|||
|
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<ul class=vector-menu-content-list>
|
|||
|
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<li id=n-mainpage class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Hauptseite?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Show main page [Alt+Shift+z]" accesskey=z><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Main page</font></font></span></a></li>
|
|||
|
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<li id=n-contents class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Wikisource:Systematik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Systematic entry</font></font></span></a></li>
|
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|
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<li id=n-Themenübersicht class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Thema?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Topic overview</font></font></span></a></li>
|
|||
|
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<li id=n-authors class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Kategorie:Autoren?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Author index</font></font></span></a></li>
|
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<li id=n-randompage class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Spezial:Zuf%C3%A4llige_Seite?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Open random page [Alt+Shift+x]" accesskey=x><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Random site</font></font></span></a></li>
|
|||
|
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</ul>
|
|||
|
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</div>
|
|||
|
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</div>
|
|||
|
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<div id=p-Mitmachen class="vector-menu mw-portlet mw-portlet-Mitmachen">
|
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|
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<div class=vector-menu-heading>
|
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|
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<font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Participants</font></font>
|
|||
|
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</div>
|
|||
|
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<div class=vector-menu-content>
|
|||
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<ul class=vector-menu-content-list>
|
|||
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<li id=n-recentchanges class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Spezial:Letzte_%C3%84nderungen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="List of recent changes to this wiki [Alt+Shift+r]" accesskey=r><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>last changes</font></font></span></a></li>
|
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|
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<li id=n-Neuer-Artikel class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Vorlage:Neuer_Artikel?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>new article</font></font></span></a></li>
|
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|
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<li id=n-Korrekturen-des-Monats class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Vorlage:Reviewtext?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Corrections of the month</font></font></span></a></li>
|
|||
|
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<li id=n-Portal class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Wikisource:Portal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Community portal</font></font></span></a></li>
|
|||
|
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<li id=n-Skriptorium class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Wikisource:Skriptorium?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Scriptorium</font></font></span></a></li>
|
|||
|
|
<li id=n-Auskunft class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Wikisource:Auskunft?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Information</font></font></span></a></li>
|
|||
|
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<li id=n-Hilfe class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Wikisource:Hilfe?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Help</font></font></span></a></li>
|
|||
|
|
<li id=n-Spenden class=mw-list-item><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-US&u=https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source%3Ddonate%26utm_medium%3Dsidebar%26utm_campaign%3DC13_de.wikisource.org%26uselang%3Dde"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Donate</font></font></span></a></li>
|
|||
|
|
</ul>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
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</div>
|
|||
|
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</div>
|
|||
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|
</div>
|
|||
|
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</nav><a href="https://de-wikisource-org.translate.goog/wiki/Hauptseite?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" class=mw-logo> <img class=mw-logo-icon src="data:image/svg+xml;base64,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
|
|||
|
|
</div>
|
|||
|
|
<div class=vector-header-end>
|
|||
|
|
<div id=p-search role=search class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"><a href="https://de-wikisource-org.translate.goog/wiki/Spezial:Suche?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle sf-hidden" title="Browse Wikisource [Alt+Shift+f]" accesskey=f> </a>
|
|||
|
|
<div class=vector-typeahead-search-container>
|
|||
|
|
<div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width">
|
|||
|
|
<form action=/w/index.php id=searchform class="cdx-search-input cdx-search-input--has-end-button">
|
|||
|
|
<div id=simpleSearch class=cdx-search-input__input-wrapper data-search-loc=header-moved>
|
|||
|
|
<div class="cdx-text-input cdx-text-input--has-start-icon"><input class=cdx-text-input__input type=search name=search placeholder="Search Wikisource" aria-label="Search Wikisource" autocapitalize=sentences title="Search Wikisource [Alt+Shift+f]" accesskey=f id=searchInput autocomplete=off value> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span>
|
|||
|
|
</div>
|
|||
|
|
</div><button class="cdx-button cdx-search-input__end-button"><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lake</font></font></button>
|
|||
|
|
</form>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools" role=navigation>
|
|||
|
|
<div class=vector-user-links-main>
|
|||
|
|
<div id=p-vector-user-menu-preferences class="vector-menu mw-portlet emptyPortlet sf-hidden">
|
|||
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|
|||
|
|
</div>
|
|||
|
|
<div id=p-vector-user-menu-userpage class="vector-menu mw-portlet emptyPortlet sf-hidden">
|
|||
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|
|||
|
|
</div>
|
|||
|
|
<nav class=vector-appearance-landmark aria-label=Appearance>
|
|||
|
|
</nav>
|
|||
|
|
<div id=p-vector-user-menu-notifications class="vector-menu mw-portlet emptyPortlet sf-hidden">
|
|||
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|
|||
|
|
</div>
|
|||
|
|
<div id=p-vector-user-menu-overflow class="vector-menu mw-portlet">
|
|||
|
|
<div class=vector-menu-content>
|
|||
|
|
<ul class=vector-menu-content-list>
|
|||
|
|
<li id=pt-createaccount-2 class="user-links-collapsible-item mw-list-item"><a data-mw=interface href="https://de-wikisource-org.translate.goog/w/index.php?title=Spezial:Benutzerkonto_anlegen&returnto=Translatorische+Bewegung+des+Licht%C3%A4thers&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="We encourage you to create an account and log in. However, it is not mandatory." data-moz-translations-id=0><span data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>create account</font></font></span></a></li>
|
|||
|
|
<li id=pt-login-2 class="user-links-collapsible-item mw-list-item"><a data-mw=interface href="https://de-wikisource-org.translate.goog/w/index.php?title=Spezial:Anmelden&returnto=Translatorische+Bewegung+des+Licht%C3%A4thers&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Registration is welcome, but is not mandatory. [Alt+Shift+o]" accesskey=o data-moz-translations-id=0><span data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>Register</font></font></span></a></li>
|
|||
|
|
</ul>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
</div>
|
|||
|
|
<div id=vector-user-links-dropdown class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="More options"><input type=checkbox id=vector-user-links-dropdown-checkbox role=button aria-haspopup=true data-event-name=ui.dropdown-vector-user-links-dropdown class=vector-dropdown-checkbox aria-label="Personal tools"> <label id=vector-user-links-dropdown-label for=vector-user-links-dropdown-checkbox class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" aria-hidden=true><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class=vector-dropdown-label-text><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Personal tools</font></font></span> </label>
|
|||
|
|
<div class=vector-dropdown-content>
|
|||
|
|
<div id=p-personal class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item sf-hidden" title="User menu">
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
</div>
|
|||
|
|
<div id=p-user-menu-anon-editor class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor">
|
|||
|
|
<div class=vector-menu-heading>
|
|||
|
|
<font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Pages for logged out users</font></font> <a href="https://de-wikisource-org.translate.goog/wiki/Hilfe:Einf%C3%BChrung?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" aria-label="Learn more about editing" data-moz-translations-id=2><span data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>More information</font></font></span></a></div>
|
|||
|
|
<div class=vector-menu-content>
|
|||
|
|
<ul class=vector-menu-content-list>
|
|||
|
|
<li id=pt-anoncontribs class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Spezial:Meine_Beitr%C3%A4ge?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="A list of edits made from this IP address [Alt+Shift+y]" accesskey=y><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Posts</font></font></span></a></li>
|
|||
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<h1 id=firstHeading class="firstHeading mw-first-heading"><span class=mw-page-title-main data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>Translational movement of the light ether</font></font></span></h1>
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<li id=ca-nstab-main class="selected vector-tab-noicon mw-list-item"><a href="https://de-wikisource-org.translate.goog/wiki/Translatorische_Bewegung_des_Licht%C3%A4thers?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Show page content [Alt+Shift+c]" accesskey=c><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Source text</font></font></span></a></li>
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<li id=ca-proofread-source class="vector-tab-noicon mw-list-item"><a title="The scanned edition was used to create this text." href="https://de-wikisource-org.translate.goog/wiki/Index:Translatorische_Bewegung_des_Licht%C3%A4thers.djvu?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>index</font></font></span></a></li>
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</div><button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name=pinnable-header.vector-page-tools.pin><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Move to sidebar</font></font></button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button sf-hidden" data-event-name=pinnable-header.vector-page-tools.unpin>Hide</button>
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<li id=t-recentchangeslinked class=mw-list-item><a href="https://de-wikisource-org.translate.goog/wiki/Spezial:%C3%84nderungen_an_verlinkten_Seiten/Translatorische_Bewegung_des_Licht%C3%A4thers?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" rel=nofollow title="Recent changes to pages linked from here [Alt+Shift+k]" accesskey=k><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Changes to Linked Sites</font></font></span></a></li>
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<li id=t-permalink class=mw-list-item><a href="https://de-wikisource-org.translate.goog/w/index.php?title=Translatorische_Bewegung_des_Licht%C3%A4thers&oldid=1857817&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Permanent link to this page version"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>permanent link</font></font></span></a></li>
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<li id=t-info class=mw-list-item><a href="https://de-wikisource-org.translate.goog/w/index.php?title=Translatorische_Bewegung_des_Licht%C3%A4thers&action=info&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="More information about this page"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Page information</font></font></span></a></li>
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<li class="mw-list-item mw-list-item-js"><a href=https://mediawiki2latex.wmflabs.org/fill/https%3A%2F%2Fde.wikisource.org%2Fwiki%2FTranslatorische_Bewegung_des_Licht%25C3%25A4thers><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Multi format export</font></font></span></a><li class="mw-list-item mw-list-item-js" id=wbc-editpage><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-US&u=https://www.wikidata.org/wiki/Special:EntityPage/Q19230778%23sitelinks-wikisource" title="Add links to pages in other languages"><span><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Add links to pages in other languages</font></font></span></a></ul>
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SHORT DESCRIPTIONSOCTIVEEntry in the : Image<table width=100% border=1 cellpadding=2 cellspacing=0 style="border-collapse:collapse;border-style:1px solid;border-color:#AAAAAA;background-color:#fff;font-size:100%;color:#191919">
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<td width=60%><b data-moz-translations-id=0><span id=ws-author data-moz-translations-id=1><a href="https://de-wikisource-org.translate.goog/wiki/Wilhelm_Wien?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Wilhelm Vienna" data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Wilhelm Vienna</font></font></a></span></b> </td>
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<td><b data-moz-translations-id=0><span id=ws-title data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>About the questions that concern the translational movement of the light ether</font></font></span></b></td>
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<td><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Annals of Physics 301 (supplement), 1898, pp. I-XVIII</font></font></td>
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<td><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>G. and E. Wiedemann</font></font></td>
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<td><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>1898</font></font></td>
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<td><span id=ws-publisher data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>John Ambr. Bart</font></font></span></td>
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<td><span id=ws-place data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>Leipzig</font></font></span></td>
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<td><span id=ws-scan data-moz-translations-id=0><a rel=nofollow class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-US&u=http://gallica.bnf.fr/ark:/12148/bpt6k153068.image.f976" data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>Gallica</font></font></a> <font style=vertical-align:inherit data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>,</font></font> <a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-US&u=https://commons.wikimedia.org/wiki/File:Translatorische_Bewegung_des_Licht%25C3%25A4thers.djvu" class=extiw title="commons:File:Translatory movement of the light ether.djvu" data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>Commons</font></font></a></span></td>
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<div class=center> <span typeof=mw:File data-moz-translations-id=0><a href="https://de-wikisource-org.translate.goog/wiki/Datei:Wikipedia-logo-v2.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" class=mw-file-description data-moz-translations-id=1><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAASCAYAAABb0P4QAAAABGdBTUEAALGPC/xhBQAAACBjSFJNAAB6JgAAgIQAAPoAAACA6AAAdTAAAOpgAAA6mAAAF3CculE8AAAABmJLR0QA/wD/AP+gvaeTAAAEQ0lEQVQ4y22UTWwVVRTHf3dm7sx7rxTaIuWrtGBCAWNLNEr81kRNWLpz48ZEQ7C4MEHUxo0LTdyZaOzKpS40aIIoRqJghChq/CgIWl7r12vBQlvem5k7c+femeuCNIHgb3Vycv7/k5yT/AXXcOLoicHG6sbE/MLSkd2PPvzWcv/UqZ+HQbNr167m0aPH7q+oHmy3272e56+7kiXPP/3EE63lWbFcTE9P39FqzX5pbbnYbE5t3bNnjwGYmZl5INfm7U67vSaMQqF1sSbLMgpT8MXnn7P55q1XcHLH2NiTFwE8gPn5+XWNRtcHg4ObuoUvTi6bAVSle0fg1iVxu3/2n9aarq4GQkAURmzbvoP+/jU9K3saP05MTGwG8AH27Xv2E6XUzqgWYY35csOGDT9v2bLlo5GRkW1zc7P1vr5eObxt+029fb04HM45SlvS3b2Cyjl0rrtzXWz99JPD74lm88978jw9aY1h6nzzwqlT38yVZRkXRfGQEIL169dP7t37zGie5zjnUEqhsoxOu01ZOZTK+P23c3iBdLnVI0F3d/2xel0SRTUOfngwybLsdiGEiKLo74GBgX+Hh4cbRVGQ5znN81NordmwcRPC86hsgR94SCkJwkhYWzwdpKl6JAgCjCkYGxsbCqQUr7366vTu3bvVvffed2eeZ+R5Tk/PKpxzLC4usX3HLeRaAwLnoH/tWlKVkar0NjEz/cdfzebU4MjoThqNOmEY0mq1kFJSr9UIpMT3fcqyoigK0jRBpYrCWjrtDp04oXKOxYUFLs1fanoOJ1euXEVZWoQQtFotrLGcO3sWKSVaF3Q6Mc45PM/DOYjqNYwxBFLieYLA9+h02mhThJ4Q4vKmwU3UanW0NvT29HBhbg7f9wlkSL1epyg0WZahVEZZlsy2Zjn9yyQCCMOQOE2pNxpEUl4IfN87niTpSGlLHA4pJbeOjgKOJIkRQhD4AWEY4nkWh2NmegatC+I0oaoclbVobfB877QHfDzdbOL5Hr7vE0URWucURYHneQSBRIYhnU6HJElQaUrXihVs27Ed4cAYQ6oUcdzBFOU73tDQ0NGNAwOTcZzgHHTiGN8P+OG77/nsyBGsvXpbAGMsZVkxODR0dXFRkGeKqqqYv3jx15dffuFbD0DKYFxKWeqiQABVVeH7AWVZkaYpxlriOKaqSnKdYa3lq+PH0FqztHQFpZT1PPfMdeEwOXnmQGnt61G9hgwCqqpChiGZUlTOkWc51hhMaUlTxW/nztLTu5rLC5ecMXZs/MUDE9cZAhw+dHi8a0X3K3039QXOOdI4wZcBVeWuflpl2LIkU4pOkqCUyopcv7B//3Nv3hBfy3z4/vt3d61a/UYQ+LsWlxaoKodzFWFYQ2uNMQVKKRYXFr+G8qXx8fGT1+pvMFzm0KFP7zKleby0dtQa0x/HnSqQ0YU8y894nv/u3r1P/fR/uv8AddhjtxLBS3EAAAAldEVYdGRhdGU6Y3JlYXRlADIwMjQtMDUtMDNUMTc6MDg6MDErMDA6MDASo2DUAAAAJXRFWHRkYXRlOm1vZGlmeQAyMDI0LTA1LTAzVDE3OjA4OjAxKzAwOjAwY/7YaAAAAABJRU5ErkJggg==" decoding=async width=20 height=18 class=mw-file-element srcset data-file-width=103 data-file-height=94 data-moz-translations-id=2 sizes></a></span><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-US&u=https://de.wikipedia.org/wiki/%25C3%2584ther_(Physik)" class=extiw title="w:ether (physics)" data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>Article in Wikipedia</font></font></a></div></td>
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<div style=font-size:80%;height:auto;color:#669966><b data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>Complete!</font></font></b> <font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>This text has been</font></font> <a href="https://de-wikisource-org.translate.goog/wiki/Hilfe:Korrekturlesen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title=Help:Proofreading data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>read twice on the basis of source correction</font></font></a> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>. The notation follows the original text.</font></font>
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<th colspan=2 bgcolor=#f9f9f9 align=center><span id=textdaten_index data-moz-translations-id=0><a href="https://de-wikisource-org.translate.goog/wiki/Index:Translatorische_Bewegung_des_Licht%C3%A4thers.djvu?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Index: Translational movement of the light ether.djvu" data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>Index page</font></font></a></span></th>
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<div class=prp-pages-output lang=de><span> <span class=pagenum id=i title="Page: Translational movement of the light ether.djvu/1" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>[</font></font> <b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/1 title="Page: Translational movement of the light ether.djvu/1" data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>i</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>]</font></font></span></span> </span>
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<div style=text-align:center;font-size:130%;line-height:20pt><b data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>On the questions concerning the translational movement of the light ether; by W. Vienna.</font></font></b></div>
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<font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>(Representation for the 70th meeting of German natural scientists and doctors in Düsseldorf, 1898; Section Physics.)</font></font>
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>The question of whether the light ether ether takes part in the movements of bodies or not, and whether mobility can be at it at all, has occupied physicists for a long time and there countless assumptions and conjectures that have been has to make about the properties of the carrier of electromagnetic phenomena held. However, there can be no doubt that everything we know about the ether is contained in</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Maxwell</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>'s theory of electromagnetism and everything else belongs to the realm of pure speculation. Accordingly, I have not set myself the task of providing a literary report on the innumerable theories that have the light ether as their subject, but have endeavored to highlight the questions that we have to answer on the basis of the basis of</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>Maxwell</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>'s theory regarding the mobility of the ether have to provide.</font></font></p>
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>If we make the assumption that the ether has mobility, further questions immediately arise, namely whether this movement requires energy expenditure, i.e. whether the ether is to be attributed inert mass, and then whether the ether the ether is also set in motion by the movement of solid bodies . The latter does not appear to be the case according to many experiments, especially after the extensive experiments of the</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Lodge</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>which were carried out with rapidly rotating metal masses or in the vicinity of high-speed circular saws.</font></font></p>
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>We will first compare the assumptions as to whether mobility can be attributed to the ether or not and then move on to the discussion of the empirical facts.</font></font></p><span style=display:none></span> <span> <span class=pagenum id=ii title="Page: Translational movement of the light ether.djvu/2" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>[</font></font> <b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/2 title="Page: Translational movement of the light ether.djvu/2" data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>ii</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>]</font></font></span></span> </span>
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|
<h3><span class=mw-headline id=Die_Annahme_der_Beweglichkeit_des_Aethers. data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>The assumption of the mobility of the aether.</font></font></span></h3>
|
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</div>
|
|||
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>The tendency to bring the properties of the ether into agreement with those of ponderable matter has led to the assumption that the ether can carry out movements in the manner of a liquid, although not a single experiment indicates the existence of such movements. But if one ascribes mobility to the ether, then, as</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Hertz</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>first noted, it follows strictly from</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>Maxwell</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>'s theory that under the influence of the pressure forces generated by a variable electromagnetic system, it must carry out movements that can be calculated, if one makes certain assumptions about the inertia of the ether.</font></font></p>
|
|||
|
|
<p><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2>Helmholtz</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>gave the basic principles for the calculation of these flows under the assumption that the inertia and compressibility of the aether is zero. However, he did not give any specific examples that would allow this theory to be tested against experience, and I will therefore give two examples from which some conclusions can be drawn as to the meaning of these assumptions.</font></font></p>
|
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|
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Currents in the ether are only excited by electromagnetic tensions when the field is neither static nor stationary, i.e. when the conditions of time are still change variable.</font></font></p>
|
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>As a first example I introduce an electrified colon, which carries equal quantities of positive and negative electricity at a very small distance from each other, which increase proportionally with time.</font></font></p>
|
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>If we designate</font> <font style=vertical-align:inherit data-moz-translations-id=2>the coordinates</font> <font style=vertical-align:inherit data-moz-translations-id=3>with x, y</font> <i data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>,</font></i></font> <i data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>z,</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=9><i data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>the time with</font></i></font> <i data-moz-translations-id=12><font style=vertical-align:inherit data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14>t</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>,</font> <i data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18>the</font></i> <font style=vertical-align:inherit data-moz-translations-id=19>components of the electrical</font> <font style=vertical-align:inherit data-moz-translations-id=20>forces with</font> <font style=vertical-align:inherit data-moz-translations-id=21>Maxwell</font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23>'s</font></span> <font style=vertical-align:inherit data-moz-translations-id=24>differential equations</font></font><i data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26></font></i><font style=vertical-align:inherit data-moz-translations-id=27></font><i data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29></font></i><font style=vertical-align:inherit data-moz-translations-id=30></font><i data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32></font></i><font style=vertical-align:inherit data-moz-translations-id=33></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35></font></span><font style=vertical-align:inherit data-moz-translations-id=36></font></p>
|
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<td valign=center style=text-align:left width=5%></td>
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<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{ll}A{\frac {dL}{dt}}={\frac {\partial Z}{\partial y}}-{\frac {\partial Y}{\partial z}}&A{\frac {dX}{dt}}={\frac {\partial M}{\partial z}}-{\frac {\partial N}{\partial y}}\\\\A{\frac {dM}{dt}}={\frac {\partial X}{\partial z}}-{\frac {\partial Z}{\partial x}}&A{\frac {dY}{dt}}={\frac {\partial N}{\partial x}}-{\frac {\partial L}{\partial z}}\\\\A{\frac {dN}{dt}}={\frac {\partial Y}{\partial x}}-{\frac {\partial X}{\partial y}}&A{\frac {dZ}{dt}}={\frac {\partial L}{\partial y}}-{\frac {\partial M}{\partial x}}\\\\{\frac {\partial L}{\partial x}}+{\frac {\partial M}{\partial y}}+{\frac {\partial N}{\partial z}}=0\ &{\frac {\partial X}{\partial x}}+{\frac {\partial Y}{\partial y}}+{\frac {\partial Z}{\partial z}}=0.\end{array}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
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<mtable columnalign="left left" rowspacing=4pt columnspacing=1em data-moz-translations-id=7>
|
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<mi data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12>
|
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A
|
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|
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<mi data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18>
|
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d
|
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</font></font></mi>
|
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<mi data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20><font style=vertical-align:inherit data-moz-translations-id=21>
|
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L
|
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</font></font></mi>
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|
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|
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<mi data-moz-translations-id=23><font style=vertical-align:inherit data-moz-translations-id=24><font style=vertical-align:inherit data-moz-translations-id=25>
|
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d
|
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</font></font></mi>
|
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|
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|
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=
|
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∂</font></font>
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Z
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∂</font></font>
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<mi data-moz-translations-id=45><font style=vertical-align:inherit data-moz-translations-id=46><font style=vertical-align:inherit data-moz-translations-id=47>
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y
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−</font></font>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59>
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Y
|
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</font></font></mi>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=64><font style=vertical-align:inherit data-moz-translations-id=65><font style=vertical-align:inherit data-moz-translations-id=66>
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e.g
|
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</font></font></mi>
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</mrow>
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</mfrac>
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</mrow>
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</mtd>
|
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<mtd data-moz-translations-id=67>
|
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<mi data-moz-translations-id=68><font style=vertical-align:inherit data-moz-translations-id=69><font style=vertical-align:inherit data-moz-translations-id=70>
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A
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</font></font></mi>
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<mfrac data-moz-translations-id=72>
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<mrow data-moz-translations-id=73>
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<mi data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75><font style=vertical-align:inherit data-moz-translations-id=76>
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d
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</font></font></mi>
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<mi data-moz-translations-id=77><font style=vertical-align:inherit data-moz-translations-id=78><font style=vertical-align:inherit data-moz-translations-id=79>
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X
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<mo data-moz-translations-id=87><font style=vertical-align:inherit data-moz-translations-id=88><font style=vertical-align:inherit data-moz-translations-id=89>
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∂</font></font>
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<mi data-moz-translations-id=96><font style=vertical-align:inherit data-moz-translations-id=97><font style=vertical-align:inherit data-moz-translations-id=98>
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|
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−</font></font>
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∂</font></font>
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|
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|
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|
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|
|
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|
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|
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|
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|
|
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|
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|
|
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|
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|
|
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|
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|
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|
|
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|
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|
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|
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|
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|
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|
|
−</font></font>
|
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|
|
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|
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|
|
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|
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|
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|
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x
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|
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|
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Y
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|
|
<mrow data-moz-translations-id=369>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=370><font style=vertical-align:inherit data-moz-translations-id=371><font style=vertical-align:inherit data-moz-translations-id=372>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=373><font style=vertical-align:inherit data-moz-translations-id=374><font style=vertical-align:inherit data-moz-translations-id=375>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=376>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=377><font style=vertical-align:inherit data-moz-translations-id=378><font style=vertical-align:inherit data-moz-translations-id=379>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=380><font style=vertical-align:inherit data-moz-translations-id=381><font style=vertical-align:inherit data-moz-translations-id=382>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=383><font style=vertical-align:inherit data-moz-translations-id=384><font style=vertical-align:inherit data-moz-translations-id=385>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=386>
|
|||
|
|
<mfrac data-moz-translations-id=387>
|
|||
|
|
<mrow data-moz-translations-id=388>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=389><font style=vertical-align:inherit data-moz-translations-id=390><font style=vertical-align:inherit data-moz-translations-id=391>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=392><font style=vertical-align:inherit data-moz-translations-id=393><font style=vertical-align:inherit data-moz-translations-id=394>
|
|||
|
|
M
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=395>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=396><font style=vertical-align:inherit data-moz-translations-id=397><font style=vertical-align:inherit data-moz-translations-id=398>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=399><font style=vertical-align:inherit data-moz-translations-id=400><font style=vertical-align:inherit data-moz-translations-id=401>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=402><font style=vertical-align:inherit data-moz-translations-id=403><font style=vertical-align:inherit data-moz-translations-id=404>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=405>
|
|||
|
|
<mfrac data-moz-translations-id=406>
|
|||
|
|
<mrow data-moz-translations-id=407>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=408><font style=vertical-align:inherit data-moz-translations-id=409><font style=vertical-align:inherit data-moz-translations-id=410>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=411><font style=vertical-align:inherit data-moz-translations-id=412><font style=vertical-align:inherit data-moz-translations-id=413>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=414>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=415><font style=vertical-align:inherit data-moz-translations-id=416><font style=vertical-align:inherit data-moz-translations-id=417>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=418><font style=vertical-align:inherit data-moz-translations-id=419><font style=vertical-align:inherit data-moz-translations-id=420>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=421><font style=vertical-align:inherit data-moz-translations-id=422><font style=vertical-align:inherit data-moz-translations-id=423>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=424><font style=vertical-align:inherit data-moz-translations-id=425><font style=vertical-align:inherit data-moz-translations-id=426>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mtext data-moz-translations-id=427>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=428>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=429>
|
|||
|
|
<mfrac data-moz-translations-id=430>
|
|||
|
|
<mrow data-moz-translations-id=431>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=432><font style=vertical-align:inherit data-moz-translations-id=433><font style=vertical-align:inherit data-moz-translations-id=434>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=435><font style=vertical-align:inherit data-moz-translations-id=436><font style=vertical-align:inherit data-moz-translations-id=437>
|
|||
|
|
X
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=438>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=439><font style=vertical-align:inherit data-moz-translations-id=440><font style=vertical-align:inherit data-moz-translations-id=441>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=442><font style=vertical-align:inherit data-moz-translations-id=443><font style=vertical-align:inherit data-moz-translations-id=444>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=445><font style=vertical-align:inherit data-moz-translations-id=446><font style=vertical-align:inherit data-moz-translations-id=447>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=448>
|
|||
|
|
<mfrac data-moz-translations-id=449>
|
|||
|
|
<mrow data-moz-translations-id=450>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=451><font style=vertical-align:inherit data-moz-translations-id=452><font style=vertical-align:inherit data-moz-translations-id=453>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=454><font style=vertical-align:inherit data-moz-translations-id=455><font style=vertical-align:inherit data-moz-translations-id=456>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=457>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=458><font style=vertical-align:inherit data-moz-translations-id=459><font style=vertical-align:inherit data-moz-translations-id=460>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=461><font style=vertical-align:inherit data-moz-translations-id=462><font style=vertical-align:inherit data-moz-translations-id=463>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=464><font style=vertical-align:inherit data-moz-translations-id=465><font style=vertical-align:inherit data-moz-translations-id=466>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=467>
|
|||
|
|
<mfrac data-moz-translations-id=468>
|
|||
|
|
<mrow data-moz-translations-id=469>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=470><font style=vertical-align:inherit data-moz-translations-id=471><font style=vertical-align:inherit data-moz-translations-id=472>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=473><font style=vertical-align:inherit data-moz-translations-id=474><font style=vertical-align:inherit data-moz-translations-id=475>
|
|||
|
|
Z
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=476>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=477><font style=vertical-align:inherit data-moz-translations-id=478><font style=vertical-align:inherit data-moz-translations-id=479>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=480><font style=vertical-align:inherit data-moz-translations-id=481><font style=vertical-align:inherit data-moz-translations-id=482>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=483><font style=vertical-align:inherit data-moz-translations-id=484><font style=vertical-align:inherit data-moz-translations-id=485>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=486><font style=vertical-align:inherit data-moz-translations-id=487><font style=vertical-align:inherit data-moz-translations-id=488>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=489><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{ll}A{\frac {dL}{dt}}={\frac {\partial Z}{\partial y}}-{\frac {\partial Y}{\partial z}}&A{\frac {dX}{dt}}={\frac {\partial M}{\partial z}}-{\frac {\partial N}{\partial y}}\\\\A{ \frac {dM}{dt}}={\frac {\partial X}{\partial z}}-{\frac {\partial Z}{\partial x}}&A{\frac {dY}{dt}} ={\frac {\partial N}{\partial x}}-{\frac {\partial L}{\partial z}}\\\\A{\frac {dN}{dt}}={\frac { \partial Y}{\partial x}}-{\frac {\partial X}{\partial y}}&A{\frac {dZ}{dt}}={\frac {\partial L}{\partial y} }-{\frac {\partial M}{\partial x}}\\\\{\frac {\partial L}{\partial x}}+{\frac {\partial M}{\partial y}}+ {\frac {\partial N}{\partial z}}=0\ &{\frac {\partial X}{\partial x}}+{\frac {\partial Y}{\partial y}}+{\ frac {\partial Z}{\partial z}}=0.\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table><span> <span class=pagenum id=iii title="Page: Translational movement of the light ether.djvu/3" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>[</font></font> <b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/3 title="Page: Translational movement of the light ether.djvu/3" data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>iii</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>]</font></font></span></span> </span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>We satisfy these equations using the following expressions:</font>
|
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|
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</font><table width=100%>
|
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<tbody>
|
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<tr>
|
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<td valign=center style=text-align:left width=5%></td>
|
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<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{lcl}X={\frac {\partial ^{2}\varphi }{\partial z\ \partial x}}&&L=-A{\frac {\partial ^{2}\varphi }{\partial y\ \partial t}}\\\\Y={\frac {\partial ^{2}\varphi }{\partial z\ \partial y}}&&M=A{\frac {\partial ^{2}\varphi }{\partial x\ \partial t}}\\\\Z={\frac {\partial ^{2}\varphi }{\partial z^{\ 2}}}&&N=0.\end{array}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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|
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<mtable columnalign="left center left" rowspacing=4pt columnspacing=1em data-moz-translations-id=7>
|
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<mtr data-moz-translations-id=8>
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<mi data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12>
|
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X
|
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</font></font></mi>
|
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<mo data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15>
|
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=
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</font></font></mo>
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<mi mathvariant=normal data-moz-translations-id=20><font style=vertical-align:inherit data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22>
|
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∂</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=23>
|
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<mn data-moz-translations-id=24><font style=vertical-align:inherit data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26>
|
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2
|
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</font></font></mn>
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|
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|
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<mi data-moz-translations-id=27><font style=vertical-align:inherit data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29>
|
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φ</font></font>
|
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</mi>
|
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|
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<mi mathvariant=normal data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33>
|
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∂</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36>
|
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e.g
|
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</font></font></mi>
|
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<mtext data-moz-translations-id=37>
|
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</mtext>
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<mi mathvariant=normal data-moz-translations-id=38><font style=vertical-align:inherit data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40>
|
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∂</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=41><font style=vertical-align:inherit data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43>
|
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x
|
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</font></font></mi>
|
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|
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</mfrac>
|
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</mrow>
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</mtd>
|
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<mtd data-moz-translations-id=44></mtd>
|
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<mtd data-moz-translations-id=45>
|
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<mi data-moz-translations-id=46><font style=vertical-align:inherit data-moz-translations-id=47><font style=vertical-align:inherit data-moz-translations-id=48>
|
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L
|
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</font></font></mi>
|
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<mo data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50><font style=vertical-align:inherit data-moz-translations-id=51>
|
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=
|
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|
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</font></font></mo>
|
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<mo data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54>
|
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−</font></font>
|
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</mo>
|
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<mi data-moz-translations-id=55><font style=vertical-align:inherit data-moz-translations-id=56><font style=vertical-align:inherit data-moz-translations-id=57>
|
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A
|
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</font></font></mi>
|
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|
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<mfrac data-moz-translations-id=59>
|
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<mrow data-moz-translations-id=60>
|
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<msup data-moz-translations-id=61>
|
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<mi mathvariant=normal data-moz-translations-id=62><font style=vertical-align:inherit data-moz-translations-id=63><font style=vertical-align:inherit data-moz-translations-id=64>
|
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∂</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
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<mn data-moz-translations-id=66><font style=vertical-align:inherit data-moz-translations-id=67><font style=vertical-align:inherit data-moz-translations-id=68>
|
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2
|
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|
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</mrow>
|
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</msup>
|
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<mi data-moz-translations-id=69><font style=vertical-align:inherit data-moz-translations-id=70><font style=vertical-align:inherit data-moz-translations-id=71>
|
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φ</font></font>
|
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|
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</mi>
|
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</mrow>
|
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<mrow data-moz-translations-id=72>
|
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<mi mathvariant=normal data-moz-translations-id=73><font style=vertical-align:inherit data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75>
|
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|
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∂</font></font>
|
|||
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</mi>
|
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<mi data-moz-translations-id=76><font style=vertical-align:inherit data-moz-translations-id=77><font style=vertical-align:inherit data-moz-translations-id=78>
|
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y
|
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</font></font></mi>
|
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<mtext data-moz-translations-id=79>
|
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</mtext>
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<mi mathvariant=normal data-moz-translations-id=80><font style=vertical-align:inherit data-moz-translations-id=81><font style=vertical-align:inherit data-moz-translations-id=82>
|
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∂</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=83><font style=vertical-align:inherit data-moz-translations-id=84><font style=vertical-align:inherit data-moz-translations-id=85>
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t
|
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|
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</font></font></mi>
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</mtd>
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</mtr>
|
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<mtr data-moz-translations-id=86>
|
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<mtd data-moz-translations-id=87></mtd>
|
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</mtr>
|
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<mtr data-moz-translations-id=88>
|
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<mtd data-moz-translations-id=89>
|
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<mi data-moz-translations-id=90><font style=vertical-align:inherit data-moz-translations-id=91><font style=vertical-align:inherit data-moz-translations-id=92>
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Y
|
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|
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</font></font></mi>
|
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<mo data-moz-translations-id=93><font style=vertical-align:inherit data-moz-translations-id=94><font style=vertical-align:inherit data-moz-translations-id=95>
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=
|
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</font></font></mo>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=96>
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<mfrac data-moz-translations-id=97>
|
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<mrow data-moz-translations-id=98>
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<msup data-moz-translations-id=99>
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<mi mathvariant=normal data-moz-translations-id=100><font style=vertical-align:inherit data-moz-translations-id=101><font style=vertical-align:inherit data-moz-translations-id=102>
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∂</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=103>
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<mn data-moz-translations-id=104><font style=vertical-align:inherit data-moz-translations-id=105><font style=vertical-align:inherit data-moz-translations-id=106>
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2
|
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</font></font></mn>
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</mrow>
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</msup>
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<mi data-moz-translations-id=107><font style=vertical-align:inherit data-moz-translations-id=108><font style=vertical-align:inherit data-moz-translations-id=109>
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φ</font></font>
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</mi>
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</mrow>
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<mi mathvariant=normal data-moz-translations-id=111><font style=vertical-align:inherit data-moz-translations-id=112><font style=vertical-align:inherit data-moz-translations-id=113>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=114><font style=vertical-align:inherit data-moz-translations-id=115><font style=vertical-align:inherit data-moz-translations-id=116>
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e.g
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</font></font></mi>
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<mtext data-moz-translations-id=117>
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<mi mathvariant=normal data-moz-translations-id=118><font style=vertical-align:inherit data-moz-translations-id=119><font style=vertical-align:inherit data-moz-translations-id=120>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=121><font style=vertical-align:inherit data-moz-translations-id=122><font style=vertical-align:inherit data-moz-translations-id=123>
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y
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</font></font></mi>
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M
|
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</font></font></mi>
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|
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</font></font></mo>
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∂</font></font>
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2
|
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φ</font></font>
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∂</font></font>
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</mi>
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∂</font></font>
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|
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<mtr data-moz-translations-id=163>
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<mtd data-moz-translations-id=164></mtd>
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Z
|
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|
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∂</font></font>
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|
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2
|
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<mi data-moz-translations-id=184><font style=vertical-align:inherit data-moz-translations-id=185><font style=vertical-align:inherit data-moz-translations-id=186>
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φ</font></font>
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∂</font></font>
|
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</mi>
|
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|
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<mi data-moz-translations-id=192><font style=vertical-align:inherit data-moz-translations-id=193><font style=vertical-align:inherit data-moz-translations-id=194>
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e.g
|
|||
|
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</font></font></mi>
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|
|
<mn data-moz-translations-id=197><font style=vertical-align:inherit data-moz-translations-id=198><font style=vertical-align:inherit data-moz-translations-id=199>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=200></mtd>
|
|||
|
|
<mtd data-moz-translations-id=201>
|
|||
|
|
<mi data-moz-translations-id=202><font style=vertical-align:inherit data-moz-translations-id=203><font style=vertical-align:inherit data-moz-translations-id=204>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=205><font style=vertical-align:inherit data-moz-translations-id=206><font style=vertical-align:inherit data-moz-translations-id=207>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=208><font style=vertical-align:inherit data-moz-translations-id=209><font style=vertical-align:inherit data-moz-translations-id=210>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=211><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{lcl}X={\frac {\partial ^{2}\varphi }{\partial z\ \partial x}}&&L=-A{\frac {\partial ^{2 }\varphi }{\partial y\ \partial t}}\\\\Y={\frac {\partial ^{2}\varphi }{\partial z\ \partial y}}&&M=A{\frac { \partial ^{2}\varphi }{\partial x\ \partial t}}\\\\Z={\frac {\partial ^{2}\varphi }{\partial z^{\ 2}}}&&N =0.\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Let a be</font></font> <i data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>a</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>constant and</font></font>
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=7><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=8><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle r^{2}=x^{2}+y^{2}+z^{2}}" data-moz-translations-id=9><semantics data-moz-translations-id=10>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=12>
|
|||
|
|
<msup data-moz-translations-id=13>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mn data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=24>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mn data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=35>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37><font style=vertical-align:inherit data-moz-translations-id=38>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mn data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41><font style=vertical-align:inherit data-moz-translations-id=42>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit data-moz-translations-id=44><font style=vertical-align:inherit data-moz-translations-id=45>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=46>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit data-moz-translations-id=48><font style=vertical-align:inherit data-moz-translations-id=49>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mn data-moz-translations-id=51><font style=vertical-align:inherit data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle r^{2}=x^{2}+y^{2}+z^{2}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=58><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=59><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varrho =x^{2}+y^{2}}" data-moz-translations-id=60><semantics data-moz-translations-id=61>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=62>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=63>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit data-moz-translations-id=65><font style=vertical-align:inherit data-moz-translations-id=66>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=67><font style=vertical-align:inherit data-moz-translations-id=68><font style=vertical-align:inherit data-moz-translations-id=69>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=70>
|
|||
|
|
<mi data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72><font style=vertical-align:inherit data-moz-translations-id=73>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=74>
|
|||
|
|
<mn data-moz-translations-id=75><font style=vertical-align:inherit data-moz-translations-id=76><font style=vertical-align:inherit data-moz-translations-id=77>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=78><font style=vertical-align:inherit data-moz-translations-id=79><font style=vertical-align:inherit data-moz-translations-id=80>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=81>
|
|||
|
|
<mi data-moz-translations-id=82><font style=vertical-align:inherit data-moz-translations-id=83><font style=vertical-align:inherit data-moz-translations-id=84>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=85>
|
|||
|
|
<mn data-moz-translations-id=86><font style=vertical-align:inherit data-moz-translations-id=87><font style=vertical-align:inherit data-moz-translations-id=88>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=89><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varrho =x^{2}+y^{2}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=93><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=94><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varphi =at/r}" data-moz-translations-id=95><semantics data-moz-translations-id=96>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=97>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=98>
|
|||
|
|
<mi data-moz-translations-id=99><font style=vertical-align:inherit data-moz-translations-id=100><font style=vertical-align:inherit data-moz-translations-id=101>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=102><font style=vertical-align:inherit data-moz-translations-id=103><font style=vertical-align:inherit data-moz-translations-id=104>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=105><font style=vertical-align:inherit data-moz-translations-id=106><font style=vertical-align:inherit data-moz-translations-id=107>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=108><font style=vertical-align:inherit data-moz-translations-id=109><font style=vertical-align:inherit data-moz-translations-id=110>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=111>
|
|||
|
|
<mo data-moz-translations-id=112><font style=vertical-align:inherit data-moz-translations-id=113><font style=vertical-align:inherit data-moz-translations-id=114>
|
|||
|
|
/
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=115><font style=vertical-align:inherit data-moz-translations-id=116><font style=vertical-align:inherit data-moz-translations-id=117>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=118><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varphi =at/r}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle at{\frac {\partial }{\partial z}}\left({\frac {1}{r}}\right).}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mfrac data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mfrac data-moz-translations-id=29>
|
|||
|
|
<mn data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37><font style=vertical-align:inherit data-moz-translations-id=38>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle at{\frac {\partial }{\partial z}}\left({\frac {1}{r}}\right).}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>This is the potential of an electric colon in the point</font></font>
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=2><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=3><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle r=0}" data-moz-translations-id=4><semantics data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=7>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12><font style=vertical-align:inherit data-moz-translations-id=13>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle r=0}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:5.31ex;height:2.176ex alt="{\displaystyle r=0}" data-moz-translations-id=18></span><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>with the positive and negative charge</font></font>
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=21><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=22><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle at/l}" data-moz-translations-id=23><semantics data-moz-translations-id=24>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=26>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36>
|
|||
|
|
/
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit data-moz-translations-id=38><font style=vertical-align:inherit data-moz-translations-id=39>
|
|||
|
|
l
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle at/l}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjMuOTI1ZXgiIGhlaWdodD0iMi44NDNleCIgc3R5bGU9InZlcnRpY2FsLWFsaWduOiAtMC44MzhleDsiIHZpZXdCb3g9IjAgLTg2My4xIDE2OTAgMTIyMy45IiByb2xlPSJpbWciIGZvY3VzYWJsZT0iZmFsc2UiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgYXJpYS1sYWJlbGxlZGJ5PSJNYXRoSmF4LVNWRy0xLVRpdGxlIj4KPHRpdGxlIGlkPSJNYXRoSmF4LVNWRy0xLVRpdGxlIj57XGRpc3BsYXlzdHlsZSBhdC9sfTwvdGl0bGU+CjxkZWZzIGFyaWEtaGlkZGVuPSJ0cnVlIj4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS02MSIgZD0iTTMzIDE1N1EzMyAyNTggMTA5IDM0OVQyODAgNDQxUTMzMSA0NDEgMzcwIDM5MlEzODYgNDIyIDQxNiA0MjJRNDI5IDQyMiA0MzkgNDE0VDQ0OSAzOTRRNDQ5IDM4MSA0MTIgMjM0VDM3NCA2OFEzNzQgNDMgMzgxIDM1VDQwMiAyNlE0MTEgMjcgNDIyIDM1UTQ0MyA1NSA0NjMgMTMxUTQ2OSAxNTEgNDczIDE1MlE0NzUgMTUzIDQ4MyAxNTNINDg3UTUwNiAxNTMgNTA2IDE0NFE1MDYgMTM4IDUwMSAxMTdUNDgxIDYzVDQ0OSAxM1E0MzYgMCA0MTcgLThRNDA5IC0xMCAzOTMgLTEwUTM1OSAtMTAgMzM2IDVUMzA2IDM2TDMwMCA1MVEyOTkgNTIgMjk2IDUwUTI5NCA0OCAyOTIgNDZRMjMzIC0xMCAxNzIgLTEwUTExNyAtMTAgNzUgMzBUMzMgMTU3Wk0zNTEgMzI4UTM1MSAzMzQgMzQ2IDM1MFQzMjMgMzg1VDI3NyA0MDVRMjQyIDQwNSAyMTAgMzc0VDE2MCAyOTNRMTMxIDIxNCAxMTkgMTI5UTExOSAxMjYgMTE5IDExOFQxMTggMTA2UTExOCA2MSAxMzYgNDRUMTc5IDI2UTIxNyAyNiAyNTQgNTlUMjk4IDExMFEzMDAgMTE0IDMyNSAyMTdUMzUxIDMyOFoiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS03NCIgZD0iTTI2IDM4NVExOSAzOTIgMTkgMzk1UTE5IDM5OSAyMiA0MTFUMjcgNDI1UTI5IDQzMCAzNiA0MzBUODcgNDMxSDE0MEwxNTkgNTExUTE2MiA1MjIgMTY2IDU0MFQxNzMgNTY2VDE3OSA1ODZUMTg3IDYwM1QxOTcgNjE1VDIxMSA2MjRUMjI5IDYyNlEyNDcgNjI1IDI1NCA2MTVUMjYxIDU5NlEyNjEgNTg5IDI1MiA1NDlUMjMyIDQ3MEwyMjIgNDMzUTIyMiA0MzEgMjcyIDQzMUgzMjNRMzMwIDQyNCAzMzAgNDIwUTMzMCAzOTggMzE3IDM4NUgyMTBMMTc0IDI0MFExMzUgODAgMTM1IDY4UTEzNSAyNiAxNjIgMjZRMTk3IDI2IDIzMCA2MFQyODMgMTQ0UTI4NSAxNTAgMjg4IDE1MVQzMDMgMTUzSDMwN1EzMjIgMTUzIDMyMiAxNDVRMzIyIDE0MiAzMTkgMTMzUTMxNCAxMTcgMzAxIDk1VDI2NyA0OFQyMTYgNlQxNTUgLTExUTEyNSAtMTEgOTggNFQ1OSA1NlE1NyA2NCA1NyA4M1YxMDFMOTIgMjQxUTEyNyAzODIgMTI4IDM4M1ExMjggMzg1IDc3IDM4NUgyNloiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTJGIiBkPSJNNDIzIDc1MFE0MzIgNzUwIDQzOCA3NDRUNDQ0IDczMFE0NDQgNzI1IDI3MSAyNDhUOTIgLTI0MFE4NSAtMjUwIDc1IC0yNTBRNjggLTI1MCA2MiAtMjQ1VDU2IC0yMzFRNTYgLTIyMSAyMzAgMjU3VDQwNyA3NDBRNDExIDc1MCA0MjMgNzUwWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTZDIiBkPSJNMTE3IDU5UTExNyAyNiAxNDIgMjZRMTc5IDI2IDIwNSAxMzFRMjExIDE1MSAyMTUgMTUyUTIxNyAxNTMgMjI1IDE1M0gyMjlRMjM4IDE1MyAyNDEgMTUzVDI0NiAxNTFUMjQ4IDE0NFEyNDcgMTM4IDI0NSAxMjhUMjM0IDkwVDIxNCA0M1QxODMgNlQxMzcgLTExUTEwMSAtMTEgNzAgMTFUMzggODVRMzggOTcgMzkgMTAyTDEwNCAzNjBRMTY3IDYxNSAxNjcgNjIzUTE2NyA2MjYgMTY2IDYyOFQxNjIgNjMyVDE1NyA2MzRUMTQ5IDYzNVQxNDEgNjM2VDEzMiA2MzdUMTIyIDYzN1ExMTIgNjM3IDEwOSA2MzdUMTAxIDYzOFQ5NSA2NDFUOTQgNjQ3UTk0IDY0OSA5NiA2NjFRMTAxIDY4MCAxMDcgNjgyVDE3OSA2ODhRMTk0IDY4OSAyMTMgNjkwVDI0MyA2OTNUMjU0IDY5NFEyNjYgNjk0IDI2NiA2ODZRMjY2IDY3NSAxOTMgMzg2VDExOCA4M1ExMTggODEgMTE4IDc1VDExNyA2NVY1OVoiPjwvcGF0aD4KPC9kZWZzPgo8ZyBzdHJva2U9ImN1cnJlbnRDb2xvciIgZmlsbD0iY3VycmVudENvbG9yIiBzdHJva2Utd2lkdGg9IjAiIHRyYW5zZm9ybT0ibWF0cml4KDEgMCAwIC0xIDAgMCkiIGFyaWEtaGlkZGVuPSJ0cnVlIj4KIDx1c2UgeGxpbms6aHJlZj0iI0UxLU1KTUFUSEktNjEiIHg9IjAiIHk9IjAiPjwvdXNlPgogPHVzZSB4bGluazpocmVmPSIjRTEtTUpNQVRISS03NCIgeD0iNTI5IiB5PSIwIj48L3VzZT4KIDx1c2UgeGxpbms6aHJlZj0iI0UxLU1KTUFJTi0yRiIgeD0iODkxIiB5PSIwIj48L3VzZT4KIDx1c2UgeGxpbms6aHJlZj0iI0UxLU1KTUFUSEktNkMiIHg9IjEzOTEiIHk9IjAiPjwvdXNlPgo8L2c+Cjwvc3ZnPg==" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:3.925ex;height:2.843ex alt="{\displaystyle at/l}" data-moz-translations-id=41></span><font style=vertical-align:inherit data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43>. The line connecting both charges</font></font>
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=44><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=45><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle l}" data-moz-translations-id=46><semantics data-moz-translations-id=47>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=48>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=49>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit data-moz-translations-id=51><font style=vertical-align:inherit data-moz-translations-id=52>
|
|||
|
|
l
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle l}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:0.693ex;height:2.176ex alt="{\displaystyle l}" data-moz-translations-id=54></span><font style=vertical-align:inherit data-moz-translations-id=55><font style=vertical-align:inherit data-moz-translations-id=56>is parallel to the</font></font> <i data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59>z</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=60><font style=vertical-align:inherit data-moz-translations-id=61>-axis. The components of</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=62><font style=vertical-align:inherit data-moz-translations-id=63><font style=vertical-align:inherit data-moz-translations-id=64>Poynting</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=65><font style=vertical-align:inherit data-moz-translations-id=66>'s energy flow are proportional to the quantities</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {P}}=ZM-YN=Aa^{2}tx\left({\frac {1}{r^{6}}}-{\frac {3z^{2}}{r^{8}}}\right)}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Z
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
M
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=18>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
|
|||
|
|
<mn data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mfrac data-moz-translations-id=28>
|
|||
|
|
<mn data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=30>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=35>
|
|||
|
|
<mfrac data-moz-translations-id=36>
|
|||
|
|
<mrow data-moz-translations-id=37>
|
|||
|
|
<mn data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=39>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
|
|||
|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=43>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mn data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {P}}=ZM-YN=Aa^{2}tx\left({\frac {1}{r^{6}}}-{\frac {3z^{2}}{ r^{8}}}\right)}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Q
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
X
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Z
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mn data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=23>
|
|||
|
|
<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mfrac data-moz-translations-id=27>
|
|||
|
|
<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=29>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mfrac data-moz-translations-id=35>
|
|||
|
|
<mrow data-moz-translations-id=36>
|
|||
|
|
<mn data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=38>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=40>
|
|||
|
|
<mn data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=42>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
|||
|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {Q}}=XN-ZL=Aa^{2}ty\left({\frac {1}{r^{6}}}-{\frac {3z^{2}}{ r^{8}}}\right)}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
X
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
M
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=18>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
|
|||
|
|
<mn data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
|
<mfrac data-moz-translations-id=25>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<msup data-moz-translations-id=27>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
|||
|
|
<mn data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=32>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=36>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {R}}=YL-XM=3Aa^{2}tz{\frac {x^{2}+y^{2}}{r^{8}}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Now let's set</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{lllll}x=\varrho \cos \vartheta &&y=\varrho \sin \vartheta &&{\frac {dx}{dt}}=\alpha ={\frac {d\varrho }{dt}}\cos \vartheta -\varrho \sin \vartheta {\frac {d\vartheta }{dt}}\\\\{\frac {d\vartheta }{dt}}=\eta &&{\frac {d\varrho }{dt}}=\zeta &&{\frac {dy}{dt}}=\beta ={\frac {d\varrho }{dt}}\sin \vartheta +\varrho \cos \vartheta {\frac {d\vartheta }{dt}}\\\\&&&&{\frac {dz}{dt}}=\gamma ,\end{array}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mtable columnalign="left left left left left" rowspacing=4pt columnspacing=1em data-moz-translations-id=7>
|
|||
|
|
<mtr data-moz-translations-id=8>
|
|||
|
|
<mtd data-moz-translations-id=9>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=16></mtd>
|
|||
|
|
<mtd data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=24></mtd>
|
|||
|
|
<mtd data-moz-translations-id=25>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mfrac data-moz-translations-id=27>
|
|||
|
|
<mrow data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=31>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mfrac data-moz-translations-id=38>
|
|||
|
|
<mrow data-moz-translations-id=39>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=42>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=53>
|
|||
|
|
<mfrac data-moz-translations-id=54>
|
|||
|
|
<mrow data-moz-translations-id=55>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=58>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=61>
|
|||
|
|
<mtd data-moz-translations-id=62></mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=63>
|
|||
|
|
<mtd data-moz-translations-id=64>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
|||
|
|
<mfrac data-moz-translations-id=66>
|
|||
|
|
<mrow data-moz-translations-id=67>
|
|||
|
|
<mi data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=70>
|
|||
|
|
<mi data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=74><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=75></mtd>
|
|||
|
|
<mtd data-moz-translations-id=76>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=77>
|
|||
|
|
<mfrac data-moz-translations-id=78>
|
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|
|
<mrow data-moz-translations-id=79>
|
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|
|
<mi data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=82>
|
|||
|
|
<mi data-moz-translations-id=83><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
d
|
|||
|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=84><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
t
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=85><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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=
|
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|
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</font></font></mo>
|
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|
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<mi data-moz-translations-id=86><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ζ</font></font>
|
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|
|
</mi>
|
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|
|
</mtd>
|
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|
|
<mtd data-moz-translations-id=87></mtd>
|
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|
|
<mtd data-moz-translations-id=88>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=89>
|
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|
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<mfrac data-moz-translations-id=90>
|
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|
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<mrow data-moz-translations-id=91>
|
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<mi data-moz-translations-id=92><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
d
|
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|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=93><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=94>
|
|||
|
|
<mi data-moz-translations-id=95><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=96><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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t
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
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|
|
<mo data-moz-translations-id=97><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
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|
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</font></font></mo>
|
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|
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<mi data-moz-translations-id=98><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
β</font></font>
|
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|
|
</mi>
|
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|
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<mo data-moz-translations-id=99><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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=
|
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|
|
</font></font></mo>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=100>
|
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|
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<mfrac data-moz-translations-id=101>
|
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|
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<mrow data-moz-translations-id=102>
|
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<mi data-moz-translations-id=103><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=104><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
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|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=105>
|
|||
|
|
<mi data-moz-translations-id=106><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
d
|
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|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=107><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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t
|
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|
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</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=108><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
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|
|
</font></font></mi>
|
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|
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<mo data-moz-translations-id=109><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
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</font></font>
|
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|
|
</mo>
|
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|
|
<mi data-moz-translations-id=110><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
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|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=111><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=112><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
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|
|
<mi data-moz-translations-id=113><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=114><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=115><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
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|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=116>
|
|||
|
|
<mfrac data-moz-translations-id=117>
|
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|
|
<mrow data-moz-translations-id=118>
|
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<mi data-moz-translations-id=119><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
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|
|
</font></font></mi>
|
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<mi data-moz-translations-id=120><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
ϑ</font></font>
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|
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</mi>
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|
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</mrow>
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|
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<mrow data-moz-translations-id=121>
|
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|
|
<mi data-moz-translations-id=122><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
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|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=123><font style=vertical-align:inherit><font style=vertical-align:inherit>
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t
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</font></font></mi>
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|
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</mrow>
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|
|
</mfrac>
|
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|
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</mrow>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=124>
|
|||
|
|
<mtd data-moz-translations-id=125></mtd>
|
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|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=126>
|
|||
|
|
<mtd data-moz-translations-id=127></mtd>
|
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|
|
<mtd data-moz-translations-id=128></mtd>
|
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|
|
<mtd data-moz-translations-id=129></mtd>
|
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|
|
<mtd data-moz-translations-id=130></mtd>
|
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|
|
<mtd data-moz-translations-id=131>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=132>
|
|||
|
|
<mfrac data-moz-translations-id=133>
|
|||
|
|
<mrow data-moz-translations-id=134>
|
|||
|
|
<mi data-moz-translations-id=135><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
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|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=136><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=137>
|
|||
|
|
<mi data-moz-translations-id=138><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=139><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=140><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=141><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=142><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=143><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{lllll}x=\varrho \cos \vartheta &&y=\varrho \sin \vartheta &&{\frac {dx}{dt}}=\alpha ={\frac {d\varrho }{dt}}\cos \vartheta -\varrho \sin \vartheta {\frac {d\vartheta }{dt}}\\\\{\frac {d\vartheta }{dt}}=\eta &&{\ frac {d\varrho }{dt}}=\zeta &&{\frac {dy}{dt}}=\beta ={\frac {d\varrho }{dt}}\sin \vartheta +\varrho \cos \ vartheta {\frac {d\vartheta }{dt}}\\\\&&&&{\frac {dz}{dt}}=\gamma ,\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>this is what the equation of incompressibility requires</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial \alpha }{\partial x}}+{\frac {\partial \beta }{\partial y}}+{\frac {\partial \gamma }{\partial z}}=0,}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mrow data-moz-translations-id=8>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<mfrac data-moz-translations-id=16>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
|
<mfrac data-moz-translations-id=25>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial \alpha }{\partial x}}+{\frac {\partial \beta }{\partial y}}+{\frac {\partial \gamma }{\partial z}} =0,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>that that</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \alpha ={\frac {\partial \psi }{\partial z}}{\frac {x}{\varrho ^{2}}}-\eta y\quad \beta ={\frac {\partial \psi }{\partial z}}{\frac {y}{\varrho ^{2}}}+\eta x\quad \gamma =-{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=16>
|
|||
|
|
<mfrac data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=19>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mspace width=1em data-moz-translations-id=26></mspace>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
|||
|
|
<mfrac data-moz-translations-id=30>
|
|||
|
|
<mrow data-moz-translations-id=31>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=34>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mfrac data-moz-translations-id=38>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=40>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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ϱ</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
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<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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2
|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
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|
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</mfrac>
|
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</mrow>
|
|||
|
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<mo data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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+
|
|||
|
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</font></font></mo>
|
|||
|
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<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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η</font></font>
|
|||
|
|
</mi>
|
|||
|
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<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mspace width=1em data-moz-translations-id=47></mspace>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
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<mo data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
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</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
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<mfrac data-moz-translations-id=52>
|
|||
|
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<mn data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mfrac data-moz-translations-id=56>
|
|||
|
|
<mrow data-moz-translations-id=57>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=60>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \alpha ={\frac {\partial \psi }{\partial z}}{\frac {x}{\varrho ^{2}}}-\eta y\quad \beta ={\frac {\ partial \psi }{\partial z}}{\frac {y}{\varrho ^{2}}}+\eta x\quad \gamma =-{\frac {1}{\varrho }}{\frac { \partial \psi }{\partial \varrho }}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>is if we assume that because of the symmetry around the</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>z</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>-axis the sizes</font></font><span class=mwe-math-element data-moz-translations-id=1><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=2><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \eta ,\zeta ,\gamma }" data-moz-translations-id=3><semantics data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ζ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \eta ,\zeta ,\gamma }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:5.595ex;height:2.676ex alt="{\displaystyle \eta ,\zeta ,\gamma }" data-moz-translations-id=13></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>independent of</font></font><span class=mwe-math-element data-moz-translat
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=19>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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ϑ</font></font>
|
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|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \vartheta }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:1.374ex;height:2.176ex alt="{\displaystyle \vartheta }" data-moz-translations-id=22></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>are.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The differential equations derived by</font> </font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Helmholtz</font></font></span><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>, which express that the electromagnetic</font></font><span data-moz-translations-id=1><span class=pagenum id=iv title="Page: Translational movement of the light ether.djvu/4" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>[</font></font> <b data-moz-translations-id=6><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/4 title="Page: Translational movement of the light ether.djvu/4" data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>iv</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>]</font></font></span> </span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Currents caused by tensions in turn produce electromagnetic forces that balance themselves with those acting from outside</font></font></p>
|
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<table width=100%>
|
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<tbody>
|
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<tr>
|
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<td valign=center style=text-align:left width=5%><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>(1)</font></font></td>
|
|||
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<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{cases}0={\frac {\partial P}{\partial x}}+A\left[{\frac {\partial {\mathfrak {P}}}{\partial t}}+\beta \left({\frac {\partial {\mathfrak {P}}}{\partial y}}-{\frac {\partial {\mathfrak {Q}}}{\partial x}}\right)-\gamma \left({\frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z}}\right)\right]\\0={\frac {\partial P}{\partial y}}+A\left[{\frac {\partial {\mathfrak {Q}}}{\partial t}}+\gamma \left({\frac {\partial {\mathfrak {Q}}}{\partial z}}-{\frac {\partial {\mathfrak {R}}}{\partial y}}\right)-\alpha \left({\frac {\partial {\mathfrak {P}}}{\partial y}}-{\frac {\partial {\mathfrak {Q}}}{\partial x}}\right)\right]\\0={\frac {\partial P}{\partial z}}+A\left[{\frac {\partial {\mathfrak {R}}}{\partial t}}+\alpha \left({\frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z}}\right)-\beta \left({\frac {\partial {\mathfrak {Q}}}{\partial z}}-{\frac {\partial {\mathfrak {R}}}{\partial y}}\right)\right]\end{cases}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
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<mrow data-moz-translations-id=7>
|
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<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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{
|
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</font></font></mo>
|
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<mtable columnalign="left left" rowspacing=.2em columnspacing=1em displaystyle=false data-moz-translations-id=9>
|
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<mtr data-moz-translations-id=10>
|
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<mtd data-moz-translations-id=11>
|
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<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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0
|
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|
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</font></font></mn>
|
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<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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=
|
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</font></font></mo>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=14>
|
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<mfrac data-moz-translations-id=15>
|
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<mrow data-moz-translations-id=16>
|
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|
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<mi mathvariant=normal data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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P
|
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|
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</font></font></mi>
|
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</mrow>
|
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<mrow data-moz-translations-id=19>
|
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<mi mathvariant=normal data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
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|
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</mi>
|
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<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
|
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|
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</font></font></mi>
|
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</mrow>
|
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</mfrac>
|
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</mrow>
|
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<mo data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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+
|
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|
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</font></font></mo>
|
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|
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<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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A
|
|||
|
|
</font></font></mi>
|
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|
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<mrow data-moz-translations-id=24>
|
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|
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<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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[
|
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|
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</font></font></mo>
|
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<mrow data-moz-translations-id=26>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
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<mfrac data-moz-translations-id=28>
|
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|
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<mrow data-moz-translations-id=29>
|
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|
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<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
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|
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<mi mathvariant=fraktur data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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P
|
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|
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</font></font></mi>
|
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|
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</mrow>
|
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|
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</mrow>
|
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|
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</mrow>
|
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<mrow data-moz-translations-id=34>
|
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<mi mathvariant=normal data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
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|
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<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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t
|
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|
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</font></font></mi>
|
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</mrow>
|
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|
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</mfrac>
|
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</mrow>
|
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<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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+
|
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|
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</font></font></mo>
|
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|
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<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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β</font></font>
|
|||
|
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</mi>
|
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|
|
<mrow data-moz-translations-id=39>
|
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|
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<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
(
|
|||
|
|
</font></font></mo>
|
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|
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<mrow data-moz-translations-id=41>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
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|
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<mfrac data-moz-translations-id=43>
|
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|
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<mrow data-moz-translations-id=44>
|
|||
|
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<mi mathvariant=normal data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
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|
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<mi mathvariant=fraktur data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
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|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=49>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
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|
|
</mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=53>
|
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|
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<mfrac data-moz-translations-id=54>
|
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|
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<mrow data-moz-translations-id=55>
|
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|
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∂</font></font>
|
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|
|
</mi>
|
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|
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|
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Q
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|
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|
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|
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∂</font></font>
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|
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|
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<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
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−</font></font>
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|
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<mi data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
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γ</font></font>
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|
|
</mi>
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∂</font></font>
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R
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∂</font></font>
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x
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−</font></font>
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0
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A
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γ</font></font>
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|
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|
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|
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|
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<mi data-moz-translations-id=160><font style=vertical-align:inherit><font style=vertical-align:inherit>
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y
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|
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|
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|
|
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−</font></font>
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|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=167>
|
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|
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Q
|
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|
|
</font></font></mi>
|
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</mrow>
|
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</mrow>
|
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</mrow>
|
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<mrow data-moz-translations-id=169>
|
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<mi mathvariant=normal data-moz-translations-id=170><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∂</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=171><font style=vertical-align:inherit><font style=vertical-align:inherit>
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x
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|
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|
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|
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|
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|
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|
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|
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|
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|
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</mtr>
|
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<mtr data-moz-translations-id=174>
|
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<mtd data-moz-translations-id=175>
|
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|
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<mn data-moz-translations-id=176><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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0
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|
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∂</font></font>
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<mi data-moz-translations-id=182><font style=vertical-align:inherit><font style=vertical-align:inherit>
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P
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∂</font></font>
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e.g
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A
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[
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∂</font></font>
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R
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∂</font></font>
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+
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α</font></font>
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∂</font></font>
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R
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∂</font></font>
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x
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−</font></font>
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∂</font></font>
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P
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∂</font></font>
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</mi>
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e.g
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</font></font></mi>
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−</font></font>
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β</font></font>
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Q
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∂</font></font>
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|
</mi>
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|
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e.g
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|
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<mo data-moz-translations-id=243><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
−</font></font>
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|
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|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=244>
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|
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|
|
<mrow data-moz-translations-id=246>
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<mi mathvariant=normal data-moz-translations-id=247><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
∂</font></font>
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|
</mi>
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|
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=249>
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|
|
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|
R
|
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|
|
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|
|
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|
|
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|
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|
|
<mrow data-moz-translations-id=251>
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|
|
<mi mathvariant=normal data-moz-translations-id=252><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
∂</font></font>
|
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=253><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
y
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|
|
</font></font></mi>
|
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|
|
</mrow>
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|
</mfrac>
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|
|
</mrow>
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|
|
</mrow>
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|
|
<mo data-moz-translations-id=254><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
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|
|
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|
|
</mrow>
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|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=255><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
]
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|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
<mo fence=true stretchy=true symmetric=true data-moz-translations-id=256></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=257><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{cases}0={\frac {\partial P}{\partial x}}+A\left[{\frac {\partial {\mathfrak {P}}}{\partial t}} +\beta \left({\frac {\partial {\mathfrak {P}}}{\partial y}}-{\frac {\partial {\mathfrak {Q}}}{\partial x}}\right) -\gamma \left({\frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z}}\right) \right]\\0={\frac {\partial P}{\partial y}}+A\left[{\frac {\partial {\mathfrak {Q}}}{\partial t}}+\gamma \ left({\frac {\partial {\mathfrak {Q}}}{\partial z}}-{\frac {\partial {\mathfrak {R}}}{\partial y}}\right)-\alpha \ left({\frac {\partial {\mathfrak {P}}}{\partial y}}-{\frac {\partial {\mathfrak {Q}}}{\partial x}}\right)\right]\ \0={\frac {\partial P}{\partial z}}+A\left[{\frac {\partial {\mathfrak {R}}}{\partial t}}+\alpha \left({\ frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z}}\right)-\beta \left({\ frac {\partial {\mathfrak {Q}}}{\partial z}}-{\frac {\partial {\mathfrak {R}}}{\partial y}}\right)\right]\end{cases} }}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Here</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>P</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>means the hydrostatic pressure.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Let us put the above values of into these equations</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {P,\ Q,\ R,}}\alpha ,\beta ,\gamma }" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo mathvariant=fraktur data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mtext mathvariant=fraktur data-moz-translations-id=10>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Q
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo mathvariant=fraktur data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mtext mathvariant=fraktur data-moz-translations-id=13>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo mathvariant=fraktur data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {P,\Q,\R,}}\alpha ,\beta ,\gamma }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 0={\frac {\partial P}{\partial \varrho }}+\varrho A^{2}a^{2}\left({\frac {3\varrho ^{2}}{r^{8}}}-{\frac {2}{r^{6}}}-{\frac {6zt}{r^{8}}}{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}\right),}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mn data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mfrac data-moz-translations-id=8>
|
|||
|
|
<mrow data-moz-translations-id=9>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mn data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=21>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=23>
|
|||
|
|
<mn data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mfrac data-moz-translations-id=29>
|
|||
|
|
<mrow data-moz-translations-id=30>
|
|||
|
|
<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=32>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=36>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
|
|||
|
|
<mfrac data-moz-translations-id=42>
|
|||
|
|
<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=44>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
|||
|
|
<mn data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mfrac data-moz-translations-id=50>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mn data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=55>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=57>
|
|||
|
|
<mn data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mfrac data-moz-translations-id=60>
|
|||
|
|
<mn data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mfrac data-moz-translations-id=64>
|
|||
|
|
<mrow data-moz-translations-id=65>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=68>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial P}{\partial \varrho }}+\varrho A^{2}a^{2}\left({\frac {3\varrho ^{2}}{r ^{8}}}-{\frac {2}{r^{6}}}-{\frac {6zt}{r^{8}}}{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}\right),}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjQ0LjYzM2V4IiBoZWlnaHQ9IjYuMzQzZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTIuNTA1ZXg7IiB2aWV3Qm94PSIwIC0xNjUyLjUgMTkyMTYuOCAyNzMwLjgiIHJvbGU9ImltZyIgZm9jdXNhYmxlPSJmYWxzZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiBhcmlhLWxhYmVsbGVkYnk9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPgo8dGl0bGUgaWQ9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPntcZGlzcGxheXN0eWxlIDA9e1xmcmFjIHtccGFydGlhbCBQfXtccGFydGlhbCBcdmFycmhvIH19K1x2YXJyaG8gQV57Mn1hXnsyfVxsZWZ0KHtcZnJhYyB7M1x2YXJyaG8gXnsyfX17cl57OH19fS17XGZyYWMgezJ9e3JeezZ9fX0te1xmcmFjIHs2enR9e3Jeezh9fX17XGZyYWMgezF9e1x2YXJyaG8gfX17XGZyYWMge1xwYXJ0aWFsIFxwc2kgfXtccGFydGlhbCBcdmFycmhvIH19XHJpZ2h0KSx9PC90aXRsZT4KPGRlZnMgYXJpYS1oaWRkZW49InRydWUiPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tMzAiIGQ9Ik05NiA1ODVRMTUyIDY2NiAyNDkgNjY2UTI5NyA2NjYgMzQ1IDY0MFQ0MjMgNTQ4UTQ2MCA0NjUgNDYwIDMyMFE0NjAgMTY1IDQxNyA4M1EzOTcgNDEgMzYyIDE2VDMwMSAtMTVUMjUwIC0yMlEyMjQgLTIyIDE5OCAtMTZUMTM3IDE2VDgyIDgzUTM5IDE2NSAzOSAzMjBRMzkgNDk0IDk2IDU4NVpNMzIxIDU5N1EyOTEgNjI5IDI1MCA2MjlRMjA4IDYyOSAxNzggNTk3UTE1MyA1NzEgMTQ1IDUyNVQxMzcgMzMzUTEzNyAxNzUgMTQ1IDEyNVQxODEgNDZRMjA5IDE2IDI1MCAxNlEyOTAgMTYgMzE4IDQ2UTM0NyA3NiAzNTQgMTMwVDM2MiAzMzNRMzYyIDQ3OCAzNTQgNTI0VDMyMSA1OTdaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0zRCIgZD0iTTU2IDM0N1E1NiAzNjAgNzAgMzY3SDcwN1E3MjIgMzU5IDcyMiAzNDdRNzIyIDMzNiA3MDggMzI4TDM5MCAzMjdINzJRNTYgMzMyIDU2IDM0N1pNNTYgMTUzUTU2IDE2OCA3MiAxNzNINzA4UTcyMiAxNjMgNzIyIDE1M1E3MjIgMTQwIDcwNyAxMzNINzBRNTYgMTQwIDU2IDE1M1oiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTIyMDIiIGQ9Ik0yMDIgNTA4UTE3OSA1MDggMTY5IDUyMFQxNTggNTQ3UTE1OCA1NTcgMTY0IDU3N1QxODUgNjI0VDIzMCA2NzVUMzAxIDcxMEwzMzMgNzE1SDM0NVEzNzggNzE1IDM4NCA3MTRRNDQ3IDcwMyA0ODkgNjYxVDU0OSA1NjhUNTY2IDQ1N1E1NjYgMzYyIDUxOSAyNDBUNDAyIDUzUTMyMSAtMjIgMjIzIC0yMlExMjMgLTIyIDczIDU2UTQyIDEwMiA0MiAxNDhWMTU5UTQyIDI3NiAxMjkgMzcwVDMyMiA0NjVRMzgzIDQ2NSA0MTQgNDM0VDQ1NSAzNjdMNDU4IDM3OFE0NzggNDYxIDQ3OCA1MTVRNDc4IDYwMyA0MzcgNjM5VDM0NCA2NzZRMjY2IDY3NiAyMjMgNjEyUTI2NCA2MDYgMjY0IDU3MlEyNjQgNTQ3IDI0NiA1MjhUMjAyIDUwOFpNNDMwIDMwNlE0MzAgMzcyIDQwMSA0MDBUMzMzIDQyOFEyNzAgNDI4IDIyMiAzODJRMTk3IDM1NCAxODMgMzIzVDE1MCAyMjFRMTMyIDE0OSAxMzIgMTE2UTEzMiAyMSAyMzIgMjFRMjQ0IDIxIDI1MCAyMlEzMjcgMzUgMzc0IDExMlEzODkgMTM3IDQwOSAxOTZUNDMwIDMwNloiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS01MCIgZD0iTTI4NyA2MjhRMjg3IDYzNSAyMzAgNjM3UTIwNiA2MzcgMTk5IDYzOFQxOTIgNjQ4UTE5MiA2NDkgMTk0IDY1OVEyMDAgNjc5IDIwMyA2ODFUMzk3IDY4M1E1ODcgNjgyIDYwMCA2ODBRNjY0IDY2OSA3MDcgNjMxVDc1MSA1MzBRNzUxIDQ1MyA2ODUgMzg5UTYxNiAzMjEgNTA3IDMwM1E1MDAgMzAyIDQwMiAzMDFIMzA3TDI3NyAxODJRMjQ3IDY2IDI0NyA1OVEyNDcgNTUgMjQ4IDU0VDI1NSA1MFQyNzIgNDhUMzA1IDQ2SDMzNlEzNDIgMzcgMzQyIDM1UTM0MiAxOSAzMzUgNVEzMzAgMCAzMTkgMFEzMTYgMCAyODIgMVQxODIgMlExMjAgMiA4NyAyVDUxIDFRMzMgMSAzMyAxMVEzMyAxMyAzNiAyNVE0MCA0MSA0NCA0M1Q2NyA0NlE5NCA0NiAxMjcgNDlRMTQxIDUyIDE0NiA2MVExNDkgNjUgMjE4IDMzOVQyODcgNjI4Wk02NDUgNTU0UTY0NSA1NjcgNjQzIDU3NVQ2MzQgNTk3VDYwOSA2MTlUNTYwIDYzNVE1NTMgNjM2IDQ4MCA2MzdRNDYzIDYzNyA0NDUgNjM3VDQxNiA2MzZUNDA0IDYzNlEzOTEgNjM1IDM4NiA2MjdRMzg0IDYyMSAzNjcgNTUwVDMzMiA0MTJUMzE0IDM0NFEzMTQgMzQyIDM5NSAzNDJINDA3SDQzMFE1NDIgMzQyIDU5MCAzOTJRNjE3IDQxOSA2MzEgNDcxVDY0NSA1NTRaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFUSEktM0YxIiBkPSJNMjA1IC0xNzRRMTM2IC0xNzQgMTAyIC0xNTNUNjcgLTc2UTY3IC0yNSA5MSA4NVQxMjcgMjM0UTE0MyAyODkgMTgyIDM0MVEyNTIgNDI3IDM0MSA0NDFRMzQzIDQ0MSAzNDkgNDQxVDM1OSA0NDJRNDMyIDQ0MiA0NzEgMzk0VDUxMCAyNzZRNTEwIDE2OSA0MzEgODBUMjUzIC0xMFEyMjYgLTEwIDIwNCAtMlQxNjkgMTlUMTQ2IDQ0VDEzMiA2NEwxMjggNzNRMTI4IDcyIDEyNCA1M1QxMTYgNVQxMTIgLTQ0UTExMiAtNjggMTE3IC03OFQxNTAgLTk1VDIzNiAtMTAyUTMyNyAtMTAyIDM1NiAtMTExVDM4NiAtMTU0UTM4NiAtMTY2IDM4NCAtMTc4UTM4MSAtMTkwIDM3OCAtMTkyVDM2MSAtMTk0SDM0OFEzNDIgLTE4OCAzNDIgLTE3OVEzNDIgLTE2OSAzMTUgLTE2OVEyOTQgLTE2OSAyNjQgLTE3MVQyMDUgLTE3NFpNNDI0IDMyMlE0MjQgMzU5IDQwNyAzODJUMzU3IDQwNVEzMjIgNDA1IDI4NyAzNzZUMjMxIDMwMFEyMjEgMjc2IDIwNCAyMTdRMTg4IDE1MiAxODggMTE2UTE4OCA2OCAyMTAgNDdUMjU5IDI2UTI5NyAyNiAzMzQgNjJRMzY3IDkyIDM4OSAxNThUNDE4IDI2NlQ0MjQgMzIyWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tMkIiIGQ9
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=18>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
|
|||
|
|
<mn data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=22>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
a
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
|
<mn data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=28>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
|||
|
|
<mfrac data-moz-translations-id=30>
|
|||
|
|
<mrow data-moz-translations-id=31>
|
|||
|
|
<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=33>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=35>
|
|||
|
|
<mn data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=37>
|
|||
|
|
<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mn data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
|
<mfrac data-moz-translations-id=43>
|
|||
|
|
<mrow data-moz-translations-id=44>
|
|||
|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=47>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mn data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=52>
|
|||
|
|
<mfrac data-moz-translations-id=53>
|
|||
|
|
<mrow data-moz-translations-id=54>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=57>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial P}{\partial z}}+zA^{2}a^{2}\left({\frac {3\varrho ^{2}}{r^{8 }}}-{\frac {6t}{r^{8}}}-{\frac {\partial \psi }{\partial z}}\right).}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjM4LjU1NWV4IiBoZWlnaHQ9IjYuMzQzZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTIuNTA1ZXg7IiB2aWV3Qm94PSIwIC0xNjUyLjUgMTY1OTkuOCAyNzMwLjgiIHJvbGU9ImltZyIgZm9jdXNhYmxlPSJmYWxzZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiBhcmlhLWxhYmVsbGVkYnk9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPgo8dGl0bGUgaWQ9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPntcZGlzcGxheXN0eWxlIDA9e1xmcmFjIHtccGFydGlhbCBQfXtccGFydGlhbCB6fX0rekFeezJ9YV57Mn1cbGVmdCh7XGZyYWMgezNcdmFycmhvIF57Mn19e3Jeezh9fX0te1xmcmFjIHs2dH17cl57OH19fS17XGZyYWMge1xwYXJ0aWFsIFxwc2kgfXtccGFydGlhbCB6fX1ccmlnaHQpLn08L3RpdGxlPgo8ZGVmcyBhcmlhLWhpZGRlbj0idHJ1ZSI+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0zMCIgZD0iTTk2IDU4NVExNTIgNjY2IDI0OSA2NjZRMjk3IDY2NiAzNDUgNjQwVDQyMyA1NDhRNDYwIDQ2NSA0NjAgMzIwUTQ2MCAxNjUgNDE3IDgzUTM5NyA0MSAzNjIgMTZUMzAxIC0xNVQyNTAgLTIyUTIyNCAtMjIgMTk4IC0xNlQxMzcgMTZUODIgODNRMzkgMTY1IDM5IDMyMFEzOSA0OTQgOTYgNTg1Wk0zMjEgNTk3UTI5MSA2MjkgMjUwIDYyOVEyMDggNjI5IDE3OCA1OTdRMTUzIDU3MSAxNDUgNTI1VDEzNyAzMzNRMTM3IDE3NSAxNDUgMTI1VDE4MSA0NlEyMDkgMTYgMjUwIDE2UTI5MCAxNiAzMTggNDZRMzQ3IDc2IDM1NCAxMzBUMzYyIDMzM1EzNjIgNDc4IDM1NCA1MjRUMzIxIDU5N1oiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTNEIiBkPSJNNTYgMzQ3UTU2IDM2MCA3MCAzNjdINzA3UTcyMiAzNTkgNzIyIDM0N1E3MjIgMzM2IDcwOCAzMjhMMzkwIDMyN0g3MlE1NiAzMzIgNTYgMzQ3Wk01NiAxNTNRNTYgMTY4IDcyIDE3M0g3MDhRNzIyIDE2MyA3MjIgMTUzUTcyMiAxNDAgNzA3IDEzM0g3MFE1NiAxNDAgNTYgMTUzWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tMjIwMiIgZD0iTTIwMiA1MDhRMTc5IDUwOCAxNjkgNTIwVDE1OCA1NDdRMTU4IDU1NyAxNjQgNTc3VDE4NSA2MjRUMjMwIDY3NVQzMDEgNzEwTDMzMyA3MTVIMzQ1UTM3OCA3MTUgMzg0IDcxNFE0NDcgNzAzIDQ4OSA2NjFUNTQ5IDU2OFQ1NjYgNDU3UTU2NiAzNjIgNTE5IDI0MFQ0MDIgNTNRMzIxIC0yMiAyMjMgLTIyUTEyMyAtMjIgNzMgNTZRNDIgMTAyIDQyIDE0OFYxNTlRNDIgMjc2IDEyOSAzNzBUMzIyIDQ2NVEzODMgNDY1IDQxNCA0MzRUNDU1IDM2N0w0NTggMzc4UTQ3OCA0NjEgNDc4IDUxNVE0NzggNjAzIDQzNyA2MzlUMzQ0IDY3NlEyNjYgNjc2IDIyMyA2MTJRMjY0IDYwNiAyNjQgNTcyUTI2NCA1NDcgMjQ2IDUyOFQyMDIgNTA4Wk00MzAgMzA2UTQzMCAzNzIgNDAxIDQwMFQzMzMgNDI4UTI3MCA0MjggMjIyIDM4MlExOTcgMzU0IDE4MyAzMjNUMTUwIDIyMVExMzIgMTQ5IDEzMiAxMTZRMTMyIDIxIDIzMiAyMVEyNDQgMjEgMjUwIDIyUTMyNyAzNSAzNzQgMTEyUTM4OSAxMzcgNDA5IDE5NlQ0MzAgMzA2WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTUwIiBkPSJNMjg3IDYyOFEyODcgNjM1IDIzMCA2MzdRMjA2IDYzNyAxOTkgNjM4VDE5MiA2NDhRMTkyIDY0OSAxOTQgNjU5UTIwMCA2NzkgMjAzIDY4MVQzOTcgNjgzUTU4NyA2ODIgNjAwIDY4MFE2NjQgNjY5IDcwNyA2MzFUNzUxIDUzMFE3NTEgNDUzIDY4NSAzODlRNjE2IDMyMSA1MDcgMzAzUTUwMCAzMDIgNDAyIDMwMUgzMDdMMjc3IDE4MlEyNDcgNjYgMjQ3IDU5UTI0NyA1NSAyNDggNTRUMjU1IDUwVDI3MiA0OFQzMDUgNDZIMzM2UTM0MiAzNyAzNDIgMzVRMzQyIDE5IDMzNSA1UTMzMCAwIDMxOSAwUTMxNiAwIDI4MiAxVDE4MiAyUTEyMCAyIDg3IDJUNTEgMVEzMyAxIDMzIDExUTMzIDEzIDM2IDI1UTQwIDQxIDQ0IDQzVDY3IDQ2UTk0IDQ2IDEyNyA0OVExNDEgNTIgMTQ2IDYxUTE0OSA2NSAyMTggMzM5VDI4NyA2MjhaTTY0NSA1NTRRNjQ1IDU2NyA2NDMgNTc1VDYzNCA1OTdUNjA5IDYxOVQ1NjAgNjM1UTU1MyA2MzYgNDgwIDYzN1E0NjMgNjM3IDQ0NSA2MzdUNDE2IDYzNlQ0MDQgNjM2UTM5MSA2MzUgMzg2IDYyN1EzODQgNjIxIDM2NyA1NTBUMzMyIDQxMlQzMTQgMzQ0UTMxNCAzNDIgMzk1IDM0Mkg0MDdINDMwUTU0MiAzNDIgNTkwIDM5MlE2MTcgNDE5IDYzMSA0NzFUNjQ1IDU1NFoiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS03QSIgZD0iTTM0NyAzMzhRMzM3IDMzOCAyOTQgMzQ5VDIzMSAzNjBRMjExIDM2MCAxOTcgMzU2VDE3NCAzNDZUMTYyIDMzNVQxNTUgMzI0TDE1MyAzMjBRMTUwIDMxNyAxMzggMzE3UTExNyAzMTcgMTE3IDMyNVExMTcgMzMwIDEyMCAzMzlRMTMzIDM3OCAxNjMgNDA2VDIyOSA0NDBRMjQxIDQ0MiAyNDYgNDQyUTI3MSA0NDIgMjkxIDQyNVQzMjkgMzkyVDM2NyAzNzVRMzg5IDM3NSA0MTEgNDA4VDQzNCA0NDFRNDM1IDQ0MiA0NDkgNDQySDQ2MlE0NjggNDM2IDQ2OCA0MzRRNDY4IDQzMCA0NjMgNDIwVDQ0OSAzOTlUNDMyIDM3N1Q0MTggMzU4TDQxMSAzNDlRMzY4IDI5OCAyNzUgMjE0VDE2MCAxMDZMMTQ4IDk0TDE2MyA5M1ExODUgOTMgMjI3IDgyVDI5MCA3MVEzMjggNzEgMzYwIDkwVDQwMiAxNDBRNDA2IDE0OSA0MDkgMTUxVDQyNCAxNTNRNDQzIDE1MyA0NDMgMTQzUTQ0MyAxMzggNDQyIDEzNFE0MjUgNzIgMzc2IDMxVDI3OCAtMTFRMjUyIC0xMSAyMzIgNlQxOTMgNDBUMTU1IDU3UTExMSA1NyA3NiAtM1E3MCAtMTEgNTkgLTExSDU0SDQxUTM1IC01IDM1IC0yUTM1IDEzIDkzIDg0UTEzMiAxMjkgMjI1IDIxNFQzNDAgMzIyUTM1MiAzMzggMzQ3IDMzOFoiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTJCIiBkPSJNNTYgMjM3VDU2IDI1MFQ3MCAyNzBIMzY5
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The angular velocity</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \eta }" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \eta }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjEuMTY5ZXgiIGhlaWdodD0iMi4xNzZleCIgc3R5bGU9InZlcnRpY2FsLWFsaWduOiAtMC44MzhleDsiIHZpZXdCb3g9IjAgLTU3Ni4xIDUwMy41IDkzNi45IiByb2xlPSJpbWciIGZvY3VzYWJsZT0iZmFsc2UiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgYXJpYS1sYWJlbGxlZGJ5PSJNYXRoSmF4LVNWRy0xLVRpdGxlIj4KPHRpdGxlIGlkPSJNYXRoSmF4LVNWRy0xLVRpdGxlIj57XGRpc3BsYXlzdHlsZSBcZXRhIH08L3RpdGxlPgo8ZGVmcyBhcmlhLWhpZGRlbj0idHJ1ZSI+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFUSEktM0I3IiBkPSJNMjEgMjg3UTIyIDI5MCAyMyAyOTVUMjggMzE3VDM4IDM0OFQ1MyAzODFUNzMgNDExVDk5IDQzM1QxMzIgNDQyUTE1NiA0NDIgMTc1IDQzNVQyMDUgNDE3VDIyMSAzOTVUMjI5IDM3NkwyMzEgMzY5UTIzMSAzNjcgMjMyIDM2N0wyNDMgMzc4UTMwNCA0NDIgMzgyIDQ0MlE0MzYgNDQyIDQ2OSA0MTVUNTAzIDMzNlYzMjZRNTAzIDMwMiA0MzkgNTNRMzgxIC0xODIgMzc3IC0xODlRMzY0IC0yMTYgMzMyIC0yMTZRMzE5IC0yMTYgMzEwIC0yMDhUMjk5IC0xODZRMjk5IC0xNzcgMzU4IDU3TDQyMCAzMDdRNDIzIDMyMiA0MjMgMzQ1UTQyMyA0MDQgMzc5IDQwNEgzNzRRMjg4IDQwNCAyMjkgMzAzTDIyMiAyOTFMMTg5IDE1N1ExNTYgMjYgMTUxIDE2UTEzOCAtMTEgMTA4IC0xMVE5NSAtMTEgODcgLTVUNzYgN1Q3NCAxN1E3NCAzMCAxMTQgMTg5VDE1NCAzNjZRMTU0IDQwNSAxMjggNDA1UTEwNyA0MDUgOTIgMzc3VDY4IDMxNlQ1NyAyODBRNTUgMjc4IDQxIDI3OEgyN1EyMSAyODQgMjEgMjg3WiI+PC9wYXRoPgo8L2RlZnM+CjxnIHN0cm9rZT0iY3VycmVudENvbG9yIiBmaWxsPSJjdXJyZW50Q29sb3IiIHN0cm9rZS13aWR0aD0iMCIgdHJhbnNmb3JtPSJtYXRyaXgoMSAwIDAgLTEgMCAwKSIgYXJpYS1oaWRkZW49InRydWUiPgogPHVzZSB4bGluazpocmVmPSIjRTEtTUpNQVRISS0zQjciIHg9IjAiIHk9IjAiPjwvdXNlPgo8L2c+Cjwvc3ZnPg==" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:1.169ex;height:2.176ex alt="{\displaystyle \eta }" data-moz-translations-id=8></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>has completely fallen out, so it does not need to have a value other than zero.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>If we eliminate</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>P</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>from this , we get</font></font></p>
|
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|
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<table width=100%>
|
|||
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<tbody>
|
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<tr>
|
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|
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<td valign=center style=text-align:left width=5%><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>(2)</font></font></td>
|
|||
|
|
<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varrho z-t{\frac {\partial \psi }{\partial \varrho }}+{\frac {8zt}{r^{2}}}\left(z{\frac {\partial \psi }{\partial \varrho }}-\varrho {\frac {\partial \psi }{\partial z}}\right)=0.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
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<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
|
<mfrac data-moz-translations-id=11>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
8th
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=25>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=31>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mfrac data-moz-translations-id=34>
|
|||
|
|
<mrow data-moz-translations-id=35>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=38>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=43>
|
|||
|
|
<mfrac data-moz-translations-id=44>
|
|||
|
|
<mrow data-moz-translations-id=45>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=48>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varrho zt{\frac {\partial \psi }{\partial \varrho }}+{\frac {8zt}{r^{2}}}\left(z{\frac {\partial \psi } {\partial \varrho }}-\varrho {\frac {\partial \psi }{\partial z}}\right)=0.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>One can see immediately from this equation that</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \psi }" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \psi }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.671ex;width:1.513ex;height:2.509ex alt="{\displaystyle \psi }" data-moz-translations-id=8></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>the factor</font></font><span class=mwe-math-element data-moz-translations-id=9><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=10><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 1/t}" data-moz-translations-id=11><semantics data-moz-translations-id=12>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=14>
|
|||
|
|
<mn data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
/
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 1/t}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:3.165ex;height:2.843ex alt="{\displaystyle 1/t}" data-moz-translations-id=20></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>must contain. For</font></font><span class=mwe-math-element data-moz-translations-id=21><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=22><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle t=0}" data-moz-translations-id=23><semantics data-moz-translations-id=24>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=26>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle t=0}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:5.101ex;height:2.176ex alt="{\displaystyle t=0}" data-moz-translations-id=31></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>the charge of the electric colon is zero. So at the moment the charge begins, the currents in the ether would become infinite.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>Since</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Maxwell</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>'s differential equations are completely fulfilled, there is no reason to exclude such a charge that increases from zero in proportion to time.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>A solution to the differential equation (2) is</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \psi ={\frac {r^{2}z}{10t}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mfrac data-moz-translations-id=13>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<msup data-moz-translations-id=15>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mn data-moz-translations-id=20><font style=vertical-align:inherit data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit data-moz-translations-id=24><font style=vertical-align:inherit data-moz-translations-id=25>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<mn data-moz-translations-id=27><font style=vertical-align:inherit data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29>
|
|||
|
|
10
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \psi ={\frac {r^{2}z}{10t}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>It follows</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \zeta ={\frac {1}{\varrho }}{\frac {\partial \psi }{\partial z}}=\left({\frac {2z^{2}+r^{2}}{10t}}\right){\frac {1}{\varrho }},}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mi data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>
|
|||
|
|
ζ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mfrac data-moz-translations-id=12>
|
|||
|
|
<mn data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23><font style=vertical-align:inherit data-moz-translations-id=24>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=28>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=38>
|
|||
|
|
<mo data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41>
|
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|
|
(
|
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|
|
</font></font></mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
|
<mfrac data-moz-translations-id=43>
|
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|
|
<mrow data-moz-translations-id=44>
|
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|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit data-moz-translations-id=46><font style=vertical-align:inherit data-moz-translations-id=47>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
|
<msup data-moz-translations-id=48>
|
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|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50><font style=vertical-align:inherit data-moz-translations-id=51>
|
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|
|
e.g
|
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|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=52>
|
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|
|
<mn data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54><font style=vertical-align:inherit data-moz-translations-id=55>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
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|
|
</msup>
|
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|
|
<mo data-moz-translations-id=56><font style=vertical-align:inherit data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58>
|
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|
|
+
|
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|
|
</font></font></mo>
|
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|
|
<msup data-moz-translations-id=59>
|
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|
|
<mi data-moz-translations-id=60><font style=vertical-align:inherit data-moz-translations-id=61><font style=vertical-align:inherit data-moz-translations-id=62>
|
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|
|
r
|
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|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
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|
|
<mn data-moz-translations-id=64><font style=vertical-align:inherit data-moz-translations-id=65><font style=vertical-align:inherit data-moz-translations-id=66>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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</mrow>
|
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|
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|
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</mrow>
|
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<mrow data-moz-translations-id=67>
|
|||
|
|
<mn data-moz-translations-id=68><font style=vertical-align:inherit data-moz-translations-id=69><font style=vertical-align:inherit data-moz-translations-id=70>
|
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|
|
10
|
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|
|
</font></font></mn>
|
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|
|
<mi data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72><font style=vertical-align:inherit data-moz-translations-id=73>
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t
|
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</font></font></mi>
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|
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</mrow>
|
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<mo data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75><font style=vertical-align:inherit data-moz-translations-id=76>
|
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)
|
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|
|
</font></font></mo>
|
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</mrow>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=77>
|
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|
|
<mfrac data-moz-translations-id=78>
|
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|
|
<mn data-moz-translations-id=79><font style=vertical-align:inherit data-moz-translations-id=80><font style=vertical-align:inherit data-moz-translations-id=81>
|
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|
|
1
|
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|
|
</font></font></mn>
|
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|
|
<mi data-moz-translations-id=82><font style=vertical-align:inherit data-moz-translations-id=83><font style=vertical-align:inherit data-moz-translations-id=84>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
</mfrac>
|
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</mrow>
|
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|
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<mo data-moz-translations-id=85><font style=vertical-align:inherit data-moz-translations-id=86><font style=vertical-align:inherit data-moz-translations-id=87>
|
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,
|
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|
|
</font></font></mo>
|
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|
|
</mstyle>
|
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|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=88><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \zeta ={\frac {1}{\varrho }}{\frac {\partial \psi }{\partial z}}=\left({\frac {2z^{2}+r^{2 }}{10t}}\right){\frac {1}{\varrho }},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjI4LjU3N2V4IiBoZWlnaHQ9IjYuMzQzZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTIuNTA1ZXg7IiB2aWV3Qm94PSIwIC0xNjUyLjUgMTIzMDQgMjczMC44IiByb2xlPSJpbWciIGZvY3VzYWJsZT0iZmFsc2UiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgYXJpYS1sYWJlbGxlZGJ5PSJNYXRoSmF4LVNWRy0xLVRpdGxlIj4KPHRpdGxlIGlkPSJNYXRoSmF4LVNWRy0xLVRpdGxlIj57XGRpc3BsYXlzdHlsZSBcemV0YSA9e1xmcmFjIHsxfXtcdmFycmhvIH19e1xmcmFjIHtccGFydGlhbCBccHNpIH17XHBhcnRpYWwgen19PVxsZWZ0KHtcZnJhYyB7MnpeezJ9K3JeezJ9fXsxMHR9fVxyaWdodCl7XGZyYWMgezF9e1x2YXJyaG8gfX0sfTwvdGl0bGU+CjxkZWZzIGFyaWEtaGlkZGVuPSJ0cnVlIj4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS0zQjYiIGQ9Ik0yOTYgNjQzUTI5OCA3MDQgMzI0IDcwNFEzNDIgNzA0IDM0MiA2ODdRMzQyIDY4MiAzMzkgNjY0VDMzNiA2MzNRMzM2IDYyMyAzMzcgNjE4VDMzOCA2MTFRMzM5IDYxMiAzNDEgNjEyUTM0MyA2MTQgMzU0IDYxNlQzNzQgNjE4TDM4NCA2MTlIMzk0UTQ3MSA2MTkgNDcxIDU4NlE0NjcgNTQ4IDM4NiA1NDZIMzcyUTMzOCA1NDYgMzIwIDU2NEwzMTEgNTU4UTIzNSA1MDYgMTc1IDM5OFQxMTQgMTkwUTExNCAxNzEgMTE2IDE1NVQxMjUgMTI3VDEzNyAxMDRUMTUzIDg2VDE3MSA3MlQxOTIgNjFUMjEzIDUzVDIzNSA0NlQyNTYgMzlMMzIyIDE2UTM4OSAtMTAgMzg5IC04MFEzODkgLTExOSAzNjQgLTE1NFQzMDAgLTIwMlEyOTIgLTIwNCAyNzQgLTIwNFEyNDcgLTIwNCAyMjUgLTE5NlEyMTAgLTE5MiAxOTMgLTE4MlQxNzIgLTE2N1ExNjcgLTE1OSAxNzMgLTE0OFExODAgLTEzOSAxOTEgLTEzOVExOTUgLTEzOSAyMjEgLTE1M1QyODMgLTE2OFEyOTggLTE2NiAzMTAgLTE1MlQzMjIgLTExN1EzMjIgLTkxIDMwMiAtNzVUMjUwIC01MVQxODMgLTI5VDExNiA0VDY1IDYyVDQ0IDE2MFE0NCAyODcgMTIxIDQxMFQyOTMgNTkwTDMwMiA1OTVRMjk2IDYxMyAyOTYgNjQzWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tM0QiIGQ9Ik01NiAzNDdRNTYgMzYwIDcwIDM2N0g3MDdRNzIyIDM1OSA3MjIgMzQ3UTcyMiAzMzYgNzA4IDMyOEwzOTAgMzI3SDcyUTU2IDMzMiA1NiAzNDdaTTU2IDE1M1E1NiAxNjggNzIgMTczSDcwOFE3MjIgMTYzIDcyMiAxNTNRNzIyIDE0MCA3MDcgMTMzSDcwUTU2IDE0MCA1NiAxNTNaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0zMSIgZD0iTTIxMyA1NzhMMjAwIDU3M1ExODYgNTY4IDE2MCA1NjNUMTAyIDU1Nkg4M1Y2MDJIMTAyUTE0OSA2MDQgMTg5IDYxN1QyNDUgNjQxVDI3MyA2NjNRMjc1IDY2NiAyODUgNjY2UTI5NCA2NjYgMzAyIDY2MFYzNjFMMzAzIDYxUTMxMCA1NCAzMTUgNTJUMzM5IDQ4VDQwMSA0Nkg0MjdWMEg0MTZRMzk1IDMgMjU3IDNRMTIxIDMgMTAwIDBIODhWNDZIMTE0UTEzNiA0NiAxNTIgNDZUMTc3IDQ3VDE5MyA1MFQyMDEgNTJUMjA3IDU3VDIxMyA2MVY1NzhaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFUSEktM0YxIiBkPSJNMjA1IC0xNzRRMTM2IC0xNzQgMTAyIC0xNTNUNjcgLTc2UTY3IC0yNSA5MSA4NVQxMjcgMjM0UTE0MyAyODkgMTgyIDM0MVEyNTIgNDI3IDM0MSA0NDFRMzQzIDQ0MSAzNDkgNDQxVDM1OSA0NDJRNDMyIDQ0MiA0NzEgMzk0VDUxMCAyNzZRNTEwIDE2OSA0MzEgODBUMjUzIC0xMFEyMjYgLTEwIDIwNCAtMlQxNjkgMTlUMTQ2IDQ0VDEzMiA2NEwxMjggNzNRMTI4IDcyIDEyNCA1M1QxMTYgNVQxMTIgLTQ0UTExMiAtNjggMTE3IC03OFQxNTAgLTk1VDIzNiAtMTAyUTMyNyAtMTAyIDM1NiAtMTExVDM4NiAtMTU0UTM4NiAtMTY2IDM4NCAtMTc4UTM4MSAtMTkwIDM3OCAtMTkyVDM2MSAtMTk0SDM0OFEzNDIgLTE4OCAzNDIgLTE3OVEzNDIgLTE2OSAzMTUgLTE2OVEyOTQgLTE2OSAyNjQgLTE3MVQyMDUgLTE3NFpNNDI0IDMyMlE0MjQgMzU5IDQwNyAzODJUMzU3IDQwNVEzMjIgNDA1IDI4NyAzNzZUMjMxIDMwMFEyMjEgMjc2IDIwNCAyMTdRMTg4IDE1MiAxODggMTE2UTE4OCA2OCAyMTAgNDdUMjU5IDI2UTI5NyAyNiAzMzQgNjJRMzY3IDkyIDM4OSAxNThUNDE4IDI2NlQ0MjQgMzIyWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tMjIwMiIgZD0iTTIwMiA1MDhRMTc5IDUwOCAxNjkgNTIwVDE1OCA1NDdRMTU4IDU1NyAxNjQgNTc3VDE4NSA2MjRUMjMwIDY3NVQzMDEgNzEwTDMzMyA3MTVIMzQ1UTM3OCA3MTUgMzg0IDcxNFE0NDcgNzAzIDQ4OSA2NjFUNTQ5IDU2OFQ1NjYgNDU3UTU2NiAzNjIgNTE5IDI0MFQ0MDIgNTNRMzIxIC0yMiAyMjMgLTIyUTEyMyAtMjIgNzMgNTZRNDIgMTAyIDQyIDE0OFYxNTlRNDIgMjc2IDEyOSAzNzBUMzIyIDQ2NVEzODMgNDY1IDQxNCA0MzRUNDU1IDM2N0w0NTggMzc4UTQ3OCA0NjEgNDc4IDUxNVE0NzggNjAzIDQzNyA2MzlUMzQ0IDY3NlEyNjYgNjc2IDIyMyA2MTJRMjY0IDYwNiAyNjQgNTcyUTI2NCA1NDcgMjQ2IDUyOFQyMDIgNTA4Wk00MzAgMzA2UTQzMCAzNzIgNDAxIDQwMFQzMzMgNDI4UTI3MCA0MjggMjIyIDM4MlExOTcgMzU0IDE4MyAzMjNUMTUwIDIyMVExMzIgMTQ5IDEzMiAxMTZRMTMyIDIxIDIzMiAyMVEyNDQgMjEgMjUwIDIyUTMyNyAzNSAzNzQgMTEyUTM4OSAxMzcgNDA5IDE5NlQ0MzAgMzA2WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTNDOCIgZD0iTTE2MSA0NDFRMjAyIDQ0MSAyMjYgNDE3VDI1MCAzNThRMjUwIDMzOCAyMTggMjUyVDE4NyAxMjdRMTkwIDg1IDIxNCA2MVEyMzUgNDMgMjU3IDM3UTI3NSAyOSAyODggMjlIMjg5TDM3MSAzNjBRNDU1IDY5MSA0NTYgNjkyUTQ1OSA2OTQgNDcyIDY5NFE0OTIgNjk0IDQ5MiA2ODdRNDkyIDY3OCA0MTEg
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<mfrac data-moz-translations-id=16>
|
|||
|
|
<mn data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=23>
|
|||
|
|
<mfrac data-moz-translations-id=24>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27><font style=vertical-align:inherit data-moz-translations-id=28>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=32>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37><font style=vertical-align:inherit data-moz-translations-id=38>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
|
<mfrac data-moz-translations-id=43>
|
|||
|
|
<mrow data-moz-translations-id=44>
|
|||
|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit data-moz-translations-id=46><font style=vertical-align:inherit data-moz-translations-id=47>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mn data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54>
|
|||
|
|
10
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=55><font style=vertical-align:inherit data-moz-translations-id=56><font style=vertical-align:inherit data-moz-translations-id=57>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59><font style=vertical-align:inherit data-moz-translations-id=60>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle -\gamma ={\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}={\frac {2z}{10t}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
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|
|
</tr>
|
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|
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</tbody>
|
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|
|
</table><span> <span class=pagenum id=v title="Page:Translatoric movement of the light ether.djvu/5" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>[</font></font> <b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/5 title="Page:Translatoric movement of the light ether.djvu/5" data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>v</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>]</font></font></span></span> </span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>So the ether would flow parallel to the streamlines,</font>
|
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</font><p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>in which the planes laid by the</font></font> <i data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>z</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>-axis are the surfaces</font></font>
|
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<span class=mwe-math-element data-moz-translations-id=7><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=8><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle r^{2}z={\rm {const.}}}" data-moz-translations-id=9><semantics data-moz-translations-id=10>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=12>
|
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<msup data-moz-translations-id=13>
|
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<mi data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>
|
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r
|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
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<mn data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>
|
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2
|
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</font></font></mn>
|
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</mrow>
|
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|
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</msup>
|
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|
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<mi data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23>
|
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e.g
|
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</font></font></mi>
|
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<mo data-moz-translations-id=24><font style=vertical-align:inherit data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26>
|
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=
|
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</font></font></mo>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
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|
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<mi mathvariant=normal data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31>
|
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c
|
|||
|
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</font></font></mi>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34>
|
|||
|
|
O
|
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|
|
</font></font></mi>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37>
|
|||
|
|
n
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=38><font style=vertical-align:inherit data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=41><font style=vertical-align:inherit data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=44><font style=vertical-align:inherit data-moz-translations-id=45><font style=vertical-align:inherit data-moz-translations-id=46>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle r^{2}z={\rm {const.}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=51><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=52><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \gamma }" data-moz-translations-id=53><semantics data-moz-translations-id=54>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=56>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \gamma }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:1.262ex;height:2.176ex alt="{\displaystyle \gamma }" data-moz-translations-id=61></span><font style=vertical-align:inherit data-moz-translations-id=62><font style=vertical-align:inherit data-moz-translations-id=63>for</font></font>
|
|||
|
|
<span class=mwe-math-element data-moz-translations-id=64><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=65><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varrho =0}" data-moz-translations-id=66><semantics data-moz-translations-id=67>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=68>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=69>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=76><font style=vertical-align:inherit data-moz-translations-id=77><font style=vertical-align:inherit data-moz-translations-id=78>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varrho =0}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.671ex;width:5.463ex;height:2.509ex alt="{\displaystyle \varrho =0}" data-moz-translations-id=80></span><font style=vertical-align:inherit data-moz-translations-id=81><font style=vertical-align:inherit data-moz-translations-id=82>becomes infinite.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>As a second case, we consider an electrified point with the charge</font></font> <i data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>e</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>, which moves through space</font> <font style=vertical-align:inherit data-moz-translations-id=7>with the constant speed</font></font> <i data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10>v</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12>. This case is completely treated by</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15>Heaviside</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17>and his solution gives the following values of the electric and magnetic forces, related to a coordinate system fixed in the electrified point in whose</font></font> <i data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>x x</font></font></i> <font style=vertical-align:inherit data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22>-axis the movement takes place.</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{lclcc}X={\frac {1}{v}}{\frac {\partial U}{\partial x}}\left(1-A^{2}v^{2}\right),&&Y={\frac {1}{v}}{\frac {\partial U}{\partial y}},&&Z={\frac {1}{v}}{\frac {\partial U}{\partial z}},\\\\M=-A{\frac {\partial U}{\partial z}},&&N=A{\frac {\partial U}{\partial y}},&&L=0.\end{array}}}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mtable columnalign="left center left center center" rowspacing=4pt columnspacing=1em data-moz-translations-id=6>
|
|||
|
|
<mtr data-moz-translations-id=7>
|
|||
|
|
<mtd data-moz-translations-id=8>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
X
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mfrac data-moz-translations-id=14>
|
|||
|
|
<mn data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mfrac data-moz-translations-id=18>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=30>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=34>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=36>
|
|||
|
|
<mn data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=40></mtd>
|
|||
|
|
<mtd data-moz-translations-id=41>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
|||
|
|
<mfrac data-moz-translations-id=45>
|
|||
|
|
<mn data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=48>
|
|||
|
|
<mfrac data-moz-translations-id=49>
|
|||
|
|
<mrow data-moz-translations-id=50>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=53>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=57></mtd>
|
|||
|
|
<mtd data-moz-translations-id=58>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Z
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=61>
|
|||
|
|
<mfrac data-moz-translations-id=62>
|
|||
|
|
<mn data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
|||
|
|
<mfrac data-moz-translations-id=66>
|
|||
|
|
<mrow data-moz-translations-id=67>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=70>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=74>
|
|||
|
|
<mtd data-moz-translations-id=75></mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=76>
|
|||
|
|
<mtd data-moz-translations-id=77>
|
|||
|
|
<mi data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
M
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=82>
|
|||
|
|
<mfrac data-moz-translations-id=83>
|
|||
|
|
<mrow data-moz-translations-id=84>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=85><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=86><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=87>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=88><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=89><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=91></mtd>
|
|||
|
|
<mtd data-moz-translations-id=92>
|
|||
|
|
<mi data-moz-translations-id=93><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=94><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=95><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=96>
|
|||
|
|
<mfrac data-moz-translations-id=97>
|
|||
|
|
<mrow data-moz-translations-id=98>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=99><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=100><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=101>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=102><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=103><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=104><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=105></mtd>
|
|||
|
|
<mtd data-moz-translations-id=106>
|
|||
|
|
<mi data-moz-translations-id=107><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=108><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=109><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=110><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{lclcc}X={\frac {1}{v}}{\frac {\partial U}{\partial x}}\left(1-A^{2}v^ {2}\right),&&Y={\frac {1}{v}}{\frac {\partial U}{\partial y}},&&Z={\frac {1}{v}}{\frac { \partial U}{\partial z}},\\\\M=-A{\frac {\partial U}{\partial z}},&&N=A{\frac {\partial U}{\partial y} },&&L=0.\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msqrt data-moz-translations-id=13>
|
|||
|
|
<msup data-moz-translations-id=14>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=16>
|
|||
|
|
<mn data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=19>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=23>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=27>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
|||
|
|
<mn data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</msqrt>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mspace width=1em data-moz-translations-id=31></mspace>
|
|||
|
|
<msup data-moz-translations-id=32>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=37>
|
|||
|
|
<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mn data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=42>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
|||
|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle U={\frac {ev}{\sqrt {r^{2}-A^{2}v^{2}\varrho ^{2}}}}\quad \varrho ^{2}=y ^{2}+z^{2}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjM1LjA5N2V4IiBoZWlnaHQ9IjYuMDA5ZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTMuMTcxZXg7IiB2aWV3Qm94PSIwIC0xMjIxLjkgMTUxMTAuOSAyNTg3LjMiIHJvbGU9ImltZyIgZm9jdXNhYmxlPSJmYWxzZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiBhcmlhLWxhYmVsbGVkYnk9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPgo8dGl0bGUgaWQ9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPntcZGlzcGxheXN0eWxlIFU9e1xmcmFjIHtldn17XHNxcnQge3JeezJ9LUFeezJ9dl57Mn1cdmFycmhvIF57Mn19fX1ccXVhZCBcdmFycmhvIF57Mn09eV57Mn0rel57Mn19PC90aXRsZT4KPGRlZnMgYXJpYS1oaWRkZW49InRydWUiPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTU1IiBkPSJNMTA3IDYzN1E3MyA2MzcgNzEgNjQxUTcwIDY0MyA3MCA2NDlRNzAgNjczIDgxIDY4MlE4MyA2ODMgOTggNjgzUTEzOSA2ODEgMjM0IDY4MVEyNjggNjgxIDI5NyA2ODFUMzQyIDY4MlQzNjIgNjgyUTM3OCA2ODIgMzc4IDY3MlEzNzggNjcwIDM3NiA2NThRMzcxIDY0MSAzNjYgNjM4SDM2NFEzNjIgNjM4IDM1OSA2MzhUMzUyIDYzOFQzNDMgNjM3VDMzNCA2MzdRMjk1IDYzNiAyODQgNjM0VDI2NiA2MjNRMjY1IDYyMSAyMzggNTE4VDE4NCAzMDJUMTU0IDE2OVExNTIgMTU1IDE1MiAxNDBRMTUyIDg2IDE4MyA1NVQyNjkgMjRRMzM2IDI0IDQwMyA2OVQ1MDEgMjA1TDU1MiA0MDZRNTk5IDU5OCA1OTkgNjA2UTU5OSA2MzMgNTM1IDYzN1E1MTEgNjM3IDUxMSA2NDhRNTExIDY1MCA1MTMgNjYwUTUxNyA2NzYgNTE5IDY3OVQ1MjkgNjgzUTUzMiA2ODMgNTYxIDY4MlQ2NDUgNjgwUTY5NiA2ODAgNzIzIDY4MVQ3NTIgNjgyUTc2NyA2ODIgNzY3IDY3MlE3NjcgNjUwIDc1OSA2NDJRNzU2IDYzNyA3MzcgNjM3UTY2NiA2MzMgNjQ4IDU5N1E2NDYgNTkyIDU5OCA0MDRRNTU3IDIzNSA1NDggMjA1UTUxNSAxMDUgNDMzIDQyVDI2MyAtMjJRMTcxIC0yMiAxMTYgMzRUNjAgMTY3VjE4M1E2MCAyMDEgMTE1IDQyMVExNjQgNjIyIDE2NCA2MjhRMTY0IDYzNSAxMDcgNjM3WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tM0QiIGQ9Ik01NiAzNDdRNTYgMzYwIDcwIDM2N0g3MDdRNzIyIDM1OSA3MjIgMzQ3UTcyMiAzMzYgNzA4IDMyOEwzOTAgMzI3SDcyUTU2IDMzMiA1NiAzNDdaTTU2IDE1M1E1NiAxNjggNzIgMTczSDcwOFE3MjIgMTYzIDcyMiAxNTNRNzIyIDE0MCA3MDcgMTMzSDcwUTU2IDE0MCA1NiAxNTNaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFUSEktNjUiIGQ9Ik0zOSAxNjhRMzkgMjI1IDU4IDI3MlQxMDcgMzUwVDE3NCA0MDJUMjQ0IDQzM1QzMDcgNDQySDMxMFEzNTUgNDQyIDM4OCA0MjBUNDIxIDM1NVE0MjEgMjY1IDMxMCAyMzdRMjYxIDIyNCAxNzYgMjIzUTEzOSAyMjMgMTM4IDIyMVExMzggMjE5IDEzMiAxODZUMTI1IDEyOFExMjUgODEgMTQ2IDU0VDIwOSAyNlQzMDIgNDVUMzk0IDExMVE0MDMgMTIxIDQwNiAxMjFRNDEwIDEyMSA0MTkgMTEyVDQyOSA5OFQ0MjAgODJUMzkwIDU1VDM0NCAyNFQyODEgLTFUMjA1IC0xMVExMjYgLTExIDgzIDQyVDM5IDE2OFpNMzczIDM1M1EzNjcgNDA1IDMwNSA0MDVRMjcyIDQwNSAyNDQgMzkxVDE5OSAzNTdUMTcwIDMxNlQxNTQgMjgwVDE0OSAyNjFRMTQ5IDI2MCAxNjkgMjYwUTI4MiAyNjAgMzI3IDI4NFQzNzMgMzUzWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTc2IiBkPSJNMTczIDM4MFExNzMgNDA1IDE1NCA0MDVRMTMwIDQwNSAxMDQgMzc2VDYxIDI4N1E2MCAyODYgNTkgMjg0VDU4IDI4MVQ1NiAyNzlUNTMgMjc4VDQ5IDI3OFQ0MSAyNzhIMjdRMjEgMjg0IDIxIDI4N1EyMSAyOTQgMjkgMzE2VDUzIDM2OFQ5NyA0MTlUMTYwIDQ0MVEyMDIgNDQxIDIyNSA0MTdUMjQ5IDM2MVEyNDkgMzQ0IDI0NiAzMzVRMjQ2IDMyOSAyMzEgMjkxVDIwMCAyMDJUMTgyIDExM1ExODIgODYgMTg3IDY5UTIwMCAyNiAyNTAgMjZRMjg3IDI2IDMxOSA2MFQzNjkgMTM5VDM5OCAyMjJUNDA5IDI3N1E0MDkgMzAwIDQwMSAzMTdUMzgzIDM0M1QzNjUgMzYxVDM1NyAzODNRMzU3IDQwNSAzNzYgNDI0VDQxNyA0NDNRNDM2IDQ0MyA0NTEgNDI1VDQ2NyAzNjdRNDY3IDM0MCA0NTUgMjg0VDQxOCAxNTlUMzQ3IDQwVDI0MSAtMTFRMTc3IC0xMSAxMzkgMjJRMTAyIDU0IDEwMiAxMTdRMTAyIDE0OCAxMTAgMTgxVDE1MSAyOThRMTczIDM2MiAxNzMgMzgwWiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTcyIiBkPSJNMjEgMjg3UTIyIDI5MCAyMyAyOTVUMjggMzE3VDM4IDM0OFQ1MyAzODFUNzMgNDExVDk5IDQzM1QxMzIgNDQyUTE2MSA0NDIgMTgzIDQzMFQyMTQgNDA4VDIyNSAzODhRMjI3IDM4MiAyMjggMzgyVDIzNiAzODlRMjg0IDQ0MSAzNDcgNDQxSDM1MFEzOTggNDQxIDQyMiA0MDBRNDMwIDM4MSA0MzAgMzYzUTQzMCAzMzMgNDE3IDMxNVQzOTEgMjkyVDM2NiAyODhRMzQ2IDI4OCAzMzQgMjk5VDMyMiAzMjhRMzIyIDM3NiAzNzggMzkyUTM1NiA0MDUgMzQyIDQwNVEyODYgNDA1IDIzOSAzMzFRMjI5IDMxNSAyMjQgMjk4VDE5MCAxNjVRMTU2IDI1IDE1MSAxNlExMzggLTExIDEwOCAtMTFROTUgLTExIDg3IC01VDc2IDdUNzQgMTdRNzQgMzAgMTE0IDE4OVQxNTQgMzY2UTE1NCA0MDUgMTI4IDQwNVExMDcgNDA1IDkyIDM3N1Q2OCAzMTZUNTcgMjgwUTU1IDI3OCA0MSAyNzhIMjdRMjEgMjg0IDIxIDI4N1oiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTMyIiBkPSJNMTA5IDQyOVE4MiA0MjkgNjYgNDQ3VDUwIDQ5MVE1MCA1NjIgMTAzIDYxNFQyMzUgNjY2UTMyNiA2NjYgMzg3IDYxMFQ0NDkgNDY1UTQ0OSA0MjIgNDI5IDM4M1QzODEgMzE1VDMwMSAyNDFRMjY1IDIxMCAyMDEgMTQ5TDE0MiA5M0wyMTggOTJRMzc1IDky
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Then the sizes result</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {P,\ Q,\ R}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo mathvariant=fraktur data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mtext mathvariant=fraktur data-moz-translations-id=10>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Q
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo mathvariant=fraktur data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mtext mathvariant=fraktur data-moz-translations-id=13>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {P,\Q,\R}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {P}}={\frac {{\mathfrak {A}}\varrho ^{2}}{\left(r^{2}-A^{2}v^{2}\varrho ^{2}\right)^{3}}},\quad {\mathfrak {Q}}=-{\frac {{\mathfrak {A}}xy}{\left(r^{2}-A^{2}v^{2}\varrho ^{2}\right)^{3}}},}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
|
<mfrac data-moz-translations-id=10>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=15>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mn data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=19>
|
|||
|
|
<mrow data-moz-translations-id=20>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<msup data-moz-translations-id=23>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=30>
|
|||
|
|
<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=32>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=36>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
|
|||
|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mspace width=1em data-moz-translations-id=44></mspace>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Q
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mfrac data-moz-translations-id=51>
|
|||
|
|
<mrow data-moz-translations-id=52>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=53>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=54>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=58>
|
|||
|
|
<mrow data-moz-translations-id=59>
|
|||
|
|
<mo data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<msup data-moz-translations-id=62>
|
|||
|
|
<mi data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=64>
|
|||
|
|
<mn data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=67>
|
|||
|
|
<mi data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=69>
|
|||
|
|
<mn data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=71>
|
|||
|
|
<mi data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=73>
|
|||
|
|
<mn data-moz-translations-id=74><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=75>
|
|||
|
|
<mi data-moz-translations-id=76><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=77>
|
|||
|
|
<mn data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=80>
|
|||
|
|
<mn data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=82><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=83><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {P}}={\frac {{\mathfrak {A}}\varrho ^{2}}{\left(r^{2}-A^{2}v^{2}\ varrho ^{2}\right)^{3}}},\quad {\mathfrak {Q}}=-{\frac {{\mathfrak {A}}xy}{\left(r^{2}-A ^{2}v^{2}\varrho ^{2}\right)^{3}}},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
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|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
</mrow>
|
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|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
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|
|
</font></font></mo>
|
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|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
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|
|
</mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
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|
|
<mfrac data-moz-translations-id=12>
|
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|
|
<mrow data-moz-translations-id=13>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=14>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
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|
<mi mathvariant=fraktur data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
A
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
</mrow>
|
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|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
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|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
e.g
|
|||
|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
|
<msup data-moz-translations-id=19>
|
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|
|
<mrow data-moz-translations-id=20>
|
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|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
(
|
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|
|
</font></font></mo>
|
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|
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<mrow data-moz-translations-id=22>
|
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<msup data-moz-translations-id=23>
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|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
r
|
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|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
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|
|
<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
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|
|
</msup>
|
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|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
−</font></font>
|
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|
|
</mo>
|
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|
|
<msup data-moz-translations-id=28>
|
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|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
A
|
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|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=30>
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<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
2
|
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|
|
</font></font></mn>
|
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</mrow>
|
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</msup>
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|
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<msup data-moz-translations-id=32>
|
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<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
v
|
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|
|
</font></font></mi>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
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|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
</mrow>
|
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</msup>
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|
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<msup data-moz-translations-id=36>
|
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|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
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|
|
<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
</mrow>
|
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|
</msup>
|
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|
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</mrow>
|
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|
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<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
)
|
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|
|
</font></font></mo>
|
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</mrow>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
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|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
3
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
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|
</msup>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
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|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
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|
|
</font></font></mo>
|
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|
|
</mstyle>
|
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|
|
</mrow>
|
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|
|
<annotation encoding=application/x-tex data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {R}}=-{\frac {{\mathfrak {A}}xz}{\left(r^{2}-A^{2}v^{2}\varrho ^{2 }\right)^{3}}},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjIzLjM1NmV4IiBoZWlnaHQ9IjYuNjc2ZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTMuMTcxZXg7IiB2aWV3Qm94PSIwIC0xNTA4LjkgMTAwNTYgMjg3NC40IiByb2xlPSJpbWciIGZvY3VzYWJsZT0iZmFsc2UiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgYXJpYS1sYWJlbGxlZGJ5PSJNYXRoSmF4LVNWRy0xLVRpdGxlIj4KPHRpdGxlIGlkPSJNYXRoSmF4LVNWRy0xLVRpdGxlIj57XGRpc3BsYXlzdHlsZSB7XG1hdGhmcmFrIHtSfX09LXtcZnJhYyB7e1xtYXRoZnJhayB7QX19eHp9e1xsZWZ0KHJeezJ9LUFeezJ9dl57Mn1cdmFycmhvIF57Mn1ccmlnaHQpXnszfX19LH08L3RpdGxlPgo8ZGVmcyBhcmlhLWhpZGRlbj0idHJ1ZSI+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KRlJBSy01MiIgZD0iTTI3IDQ5NlEzMSA1NjkgMTAyIDYyN1QyMzQgNjg1UTIzNiA2ODUgMjQxIDY4NVQyNTEgNjg2UTI4NyA2ODYgMzE4IDY3MlQzNjcgNjM4VDM5OSA1OThUNDE4IDU2NEw0MjMgNTUwUTQyNCA1NTQgNDM0IDU2N1Q0NjMgNjAxVDUwNSA2MzlUNTYxIDY3MVQ2MjYgNjg1UTY3MiA2ODUgNjg4IDY1OVQ3MTAgNTcyUTcxMyA1MzMgNzIxIDUyM1Q3NjYgNTEzUTc4MSA1MTMgNzg3IDUxNFQ3OTQgNTE2UTc5NiA1MTIgNzk4IDUwOVQ4MDEgNTA0VDgwMiA1MDFUNzg3IDQ5M1E3MDIgNDYxIDYyNCA0MDFMNjA3IDM4OVE2NTUgMzgzIDY4OCAzNThMNjk3IDM1MlYzNDJRNjk5IDMzMCA2OTkgMjk3UTcwNCAyMDkgNzEwIDE3M1Q3MzQgMTAzUTc1MSA2OSA3NjUgNjlRNzY5IDY5IDgwNiA4M0w4MjQgOTBWNzRRODIzIDczIDc1OSAyNFQ2OTMgLTI2UTY5MiAtMjYgNjYwIDMyTDYyOCA5MEw2MjkgMTExUTYzMSAxNTkgNjMxIDE3N1E2MzEgMjc4IDYxNCAzMDBRNTg0IDM0MCA1MjMgMzQwUTUwMCAzNDAgNDY3IDMzM1Q0MzEgMzI1UTQyOSAzMjUgNDI5IDMyMlE0MjggMzIxIDQyNiAzMDhUNDIwIDI3NVQ0MTAgMjMwVDM5MiAxNzhUMzY2IDEyNUwzNTggMTEyTDM0MiA5OVEzMDYgNzAgMjY5IDM4VDIxMyAtMTBUMTkzIC0yNlExOTIgLTI2IDE2MyAwVDExNiAyNlE4MiAyNiA1MCAtOEw0MiAtMTZMMzUgLThMMjcgMEwzNSAxMFE0MyAyMSA1OCAzOFQxMDQgODBUMTU4IDEwNlExNzkgMTA2IDIxOCA2NUwyMzUgNDhRMjM4IDQ4IDI1NSA2MFQyOTUgOTlUMzI5IDE1OFEzNTIgMjMxIDM1MiAzNTlRMzUyIDU1NSAyNDIgNjE0UTIxMCA2MjggMTg3IDYyOFExNDAgNjI4IDExNiA2MDBUOTEgNTQ4UTkxIDUyMiAxMzggNDY0VDE4NSAzODJWMzc2UTE4NSAzNDUgMTU4IDMxM1QxMDMgMjYzTDc2IDI0NlE3NCAyNDQgNjQgMjUzTDU0IDI2MEw2NSAyNjdROTEgMjg1IDEwMCAzMDJRMTExIDMxOCAxMTEgMzM3UTExMSAzNTUgNjkgNDEwVDI3IDQ5NlpNNTYyIDYyOFE1MDQgNjI4IDQ0MyA1MDdMNDM1IDQ5MUw0MzYgNDc5UTQzNyA0NzEgNDM3IDQ0NlE0MzcgMzk2IDQzMiAzNTFMNTI5IDM4OUw2MDIgNDI2UTY3MyA0NjIgNjczIDQ2M0g2NzJRNjQ0IDQ3MCA2MzcgNDgzVDYyMiA1NTNRNjA4IDYyOCA1NjIgNjI4WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tM0QiIGQ9Ik01NiAzNDdRNTYgMzYwIDcwIDM2N0g3MDdRNzIyIDM1OSA3MjIgMzQ3UTcyMiAzMzYgNzA4IDMyOEwzOTAgMzI3SDcyUTU2IDMzMiA1NiAzNDdaTTU2IDE1M1E1NiAxNjggNzIgMTczSDcwOFE3MjIgMTYzIDcyMiAxNTNRNzIyIDE0MCA3MDcgMTMzSDcwUTU2IDE0MCA1NiAxNTNaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0yMjEyIiBkPSJNODQgMjM3VDg0IDI1MFQ5OCAyNzBINjc5UTY5NCAyNjIgNjk0IDI1MFQ2NzkgMjMwSDk4UTg0IDIzNyA4NCAyNTBaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KRlJBSy00MSIgZD0iTTIyIDUwNVEyMiA1NjMgOTQgNjI0VDI3MSA2ODVIMjgwUTQxNiA2ODUgNDQzIDU2MFE0NDcgNTM1IDQ0NyA1MDRRNDQ0IDQxNCA0MDUgMzMwTDM5OSAzMTlMMjI5IDE1NVEyMzMgMTU0IDI0MSAxNTNUMjUzIDE1MFQyNjUgMTQ1VDI4MSAxMzVUMzAxIDExOVQzMjggOTNMMzU3IDY0TDQwMiA5MlE0MzggMTE2IDQ3MyAxMzdMNTAwIDE1NFYzMzlRNTAwIDUyOCA0OTUgNTkzVjYwMUw1NTkgNjQ5UTYyMSA2OTYgNjI0IDY5Nkw2MzggNjg2TDYyOSA2NzdRNTk5IDY1MCA1OTMgNjM4UTU4MiA2MTQgNTgxIDUwNFE1ODAgNDkwIDU4MCA0NDNRNTgwIDMxNCA1ODQgMjM4UTU4NCAyMzUgNTg0IDIyNFQ1ODQgMjEwVDU4NSAxOTlUNTg2IDE4N1Q1ODggMTc2VDU5MSAxNjRUNTk1IDE1MlQ2MDEgMTM3VDYwOSAxMjFRNjMwIDc3IDY0MCA3N1E2NjEgNzcgNzAzIDEwMVE3MDQgOTUgNzA2IDkwTDcwNyA4NlY4NEw2MzYgMjlRNjE4IDE1IDYwMSAyVDU3NCAtMTlUNTY0IC0yNUw1MDAgMTIxUTQ5OSAxMjEgMzk5IDQ4TDI5OSAtMjZRMjk4IC0yNiAyOTEgLTE1VDI3MiAxMVQyNDUgNDJUMjA5IDY5VDE2NSA4MFExMjAgODAgNTggNDNMNDggMzdMNDAgNDJMMzIgNDhMMTIyIDExN1ExOTYgMTczIDI0MSAyMTFRMzE5IDI4MCAzNDMgMzI3VDM2OCA0NDdRMzY4IDUzNSAzMTcgNTgyUTI2NCA2MzMgMTk5IDYzM1ExNTUgNjMzIDEyMiA2MDVUODYgNTQyUTg2IDUxOCAxMzMgNDY3VDE4MSAzODdRMTgxIDM0OCAxNDAgMzA5UTExMyAyODEgNzMgMjYwTDY0IDI1NUw1MCAyNjVMNTkgMjczUTExMiAzMDcgMTEyIDM0NVExMTIgMzYzIDkwIDM4N1Q0NSA0NDFUMjIgNTA1WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BVEhJLTc4IiBkPSJNNTIgMjg5UTU5IDMzMSAxMDYgMzg2VDIyMiA0NDJRMjU3IDQ0MiAyODYgNDI0VDMyOSAzNzlRMzcxIDQ0MiA0MzAgNDQyUTQ2NyA0NDIgNDk0IDQyMFQ1MjIgMzYxUTUyMiAzMzIgNTA4IDMxNFQ0ODEgMjkyVDQ1OCAyODhRNDM5IDI4OCA0MjcgMjk5VDQxNSAzMjhRNDE1IDM3NCA0NjUgMzkxUTQ1NCA0MDQgNDI1IDQw
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=10>
|
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|
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<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mn data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mn data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=21>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=23>
|
|||
|
|
<mn data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=25>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {A}}=e^{2}vA\left(1-A^{2}v^{2}\right).}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Let's sit again</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \alpha =-{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }},\quad \beta ={\frac {\partial \psi }{\partial x}}{\frac {y}{\varrho ^{2}}}+\eta z,\quad \gamma ={\frac {\partial \psi }{\partial x}}{\frac {z}{\varrho ^{2}}}-\eta y,}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
|
<mfrac data-moz-translations-id=10>
|
|||
|
|
<mn data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mfrac data-moz-translations-id=14>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
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|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mspace width=1em data-moz-translations-id=22></mspace>
|
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|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mfrac data-moz-translations-id=26>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=30>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mfrac data-moz-translations-id=34>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=36>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
2
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
|||
|
|
</msup>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mspace width=1em data-moz-translations-id=44></mspace>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
|||
|
|
<mfrac data-moz-translations-id=48>
|
|||
|
|
<mrow data-moz-translations-id=49>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
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|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=52>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mfrac data-moz-translations-id=56>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=58>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=60>
|
|||
|
|
<mn data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
η</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \alpha =-{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }},\quad \beta ={\frac {\partial \psi }{ \partial x}}{\frac {y}{\varrho ^{2}}}+\eta z,\quad \gamma ={\frac {\partial \psi }{\partial x}}{\frac {z }{\varrho ^{2}}}-\eta y,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=72>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=73>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=74>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=75>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=76><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=78>
|
|||
|
|
<mfrac data-moz-translations-id=79>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=80>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=82>
|
|||
|
|
<mrow data-moz-translations-id=83>
|
|||
|
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<mo data-moz-translations-id=84><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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(
|
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|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=85>
|
|||
|
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<msup data-moz-translations-id=86>
|
|||
|
|
<mi data-moz-translations-id=87><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=88>
|
|||
|
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<mn data-moz-translations-id=89><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=91>
|
|||
|
|
<mi data-moz-translations-id=92><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=93>
|
|||
|
|
<mn data-moz-translations-id=94><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=95>
|
|||
|
|
<mi data-moz-translations-id=96><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=97>
|
|||
|
|
<mn data-moz-translations-id=98><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=99>
|
|||
|
|
<mi data-moz-translations-id=100><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=101>
|
|||
|
|
<mn data-moz-translations-id=102><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=103><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=104>
|
|||
|
|
<mn data-moz-translations-id=105><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=106><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=107><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {S}}={\frac {\mathfrak {A}}{\left(r^{2}-A^{2}v^{2}\varrho ^{2}\right) ^{3}}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>so we get from equations (1)</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 0={\frac {\partial P}{\partial \varrho }}+A\left(-v{\frac {\partial {\mathfrak {S}}}{\partial x}}x\varrho -\varrho v{\mathfrak {S}}+{\frac {\partial \psi }{\partial \varrho }}\left[3{\mathfrak {S}}+x{\frac {\partial {\mathfrak {S}}}{\partial x}}+\varrho {\frac {\partial {\mathfrak {S}}}{\partial \varrho }}\right]\right),}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mn data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mfrac data-moz-translations-id=8>
|
|||
|
|
<mrow data-moz-translations-id=9>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=22>
|
|||
|
|
<mfrac data-moz-translations-id=23>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43><font style=vertical-align:inherit data-moz-translations-id=44>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mfrac data-moz-translations-id=46>
|
|||
|
|
<mrow data-moz-translations-id=47>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=48><font style=vertical-align:inherit data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=51><font style=vertical-align:inherit data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=54>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=55><font style=vertical-align:inherit data-moz-translations-id=56><font style=vertical-align:inherit data-moz-translations-id=57>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59><font style=vertical-align:inherit data-moz-translations-id=60>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<mo data-moz-translations-id=62><font style=vertical-align:inherit data-moz-translations-id=63><font style=vertical-align:inherit data-moz-translations-id=64>
|
|||
|
|
[
|
|||
|
|
</font></font></mo>
|
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|
|
<mrow data-moz-translations-id=65>
|
|||
|
|
<mn data-moz-translations-id=66><font style=vertical-align:inherit data-moz-translations-id=67><font style=vertical-align:inherit data-moz-translations-id=68>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=69>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=70>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72><font style=vertical-align:inherit data-moz-translations-id=73>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75><font style=vertical-align:inherit data-moz-translations-id=76>
|
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|
|
+
|
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|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=77><font style=vertical-align:inherit data-moz-translations-id=78><font style=vertical-align:inherit data-moz-translations-id=79>
|
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|
|
x
|
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|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=80>
|
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|
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<mfrac data-moz-translations-id=81>
|
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|
|
<mrow data-moz-translations-id=82>
|
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|
|
<mi mathvariant=normal data-moz-translations-id=83><font style=vertical-align:inherit data-moz-translations-id=84><font style=vertical-align:inherit data-moz-translations-id=85>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=86>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=87>
|
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|
|
<mi mathvariant=fraktur data-moz-translations-id=88><font style=vertical-align:inherit data-moz-translations-id=89><font style=vertical-align:inherit data-moz-translations-id=90>
|
|||
|
|
S
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=91>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=92><font style=vertical-align:inherit data-moz-translations-id=93><font style=vertical-align:inherit data-moz-translations-id=94>
|
|||
|
|
∂</font></font>
|
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|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=95><font style=vertical-align:inherit data-moz-translations-id=96><font style=vertical-align:inherit data-moz-translations-id=97>
|
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|
|
x
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
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|
|
<mo data-moz-translations-id=98><font style=vertical-align:inherit data-moz-translations-id=99><font style=vertical-align:inherit data-moz-translations-id=100>
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|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=101><font style=vertical-align:inherit data-moz-translations-id=102><font style=vertical-align:inherit data-moz-translations-id=103>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=104>
|
|||
|
|
<mfrac data-moz-translations-id=105>
|
|||
|
|
<mrow data-moz-translations-id=106>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=107><font style=vertical-align:inherit data-moz-translations-id=108><font style=vertical-align:inherit data-moz-translations-id=109>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=110>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=111>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=112><font style=vertical-align:inherit data-moz-translations-id=113><font style=vertical-align:inherit data-moz-translations-id=114>
|
|||
|
|
S
|
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|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=115>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=116><font style=vertical-align:inherit data-moz-translations-id=117><font style=vertical-align:inherit data-moz-translations-id=118>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=119><font style=vertical-align:inherit data-moz-translations-id=120><font style=vertical-align:inherit data-moz-translations-id=121>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=122><font style=vertical-align:inherit data-moz-translations-id=123><font style=vertical-align:inherit data-moz-translations-id=124>
|
|||
|
|
]
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=125><font style=vertical-align:inherit data-moz-translations-id=126><font style=vertical-align:inherit data-moz-translations-id=127>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=128><font style=vertical-align:inherit data-moz-translations-id=129><font style=vertical-align:inherit data-moz-translations-id=130>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=131><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial P}{\partial \varrho }}+A\left(-v{\frac {\partial {\mathfrak {S}}}{\partial x}}x\varrho -\varrho v{\mathfrak {S}}+{\frac {\partial \psi }{\partial \varrho }}\left[3{\mathfrak {S}}+x{\frac {\partial {\mathfrak {S}}}{\partial x}}+\varrho {\frac {\partial {\mathfrak {S}}}{\partial \varrho }}\right]\right),}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mfrac data-moz-translations-id=13>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19><font style=vertical-align:inherit data-moz-translations-id=20>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23><font style=vertical-align:inherit data-moz-translations-id=24>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=34>
|
|||
|
|
<mo data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=38>
|
|||
|
|
<mo data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40><font style=vertical-align:inherit data-moz-translations-id=41>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43><font style=vertical-align:inherit data-moz-translations-id=44>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mfrac data-moz-translations-id=46>
|
|||
|
|
<mrow data-moz-translations-id=47>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=48><font style=vertical-align:inherit data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=52>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54><font style=vertical-align:inherit data-moz-translations-id=55>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=56>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=60><font style=vertical-align:inherit data-moz-translations-id=61><font style=vertical-align:inherit data-moz-translations-id=62>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=63>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit data-moz-translations-id=65><font style=vertical-align:inherit data-moz-translations-id=66>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=67>
|
|||
|
|
<mn data-moz-translations-id=68><font style=vertical-align:inherit data-moz-translations-id=69><font style=vertical-align:inherit data-moz-translations-id=70>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72><font style=vertical-align:inherit data-moz-translations-id=73>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=74>
|
|||
|
|
<mfrac data-moz-translations-id=75>
|
|||
|
|
<mrow data-moz-translations-id=76>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=77><font style=vertical-align:inherit data-moz-translations-id=78><font style=vertical-align:inherit data-moz-translations-id=79>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=80><font style=vertical-align:inherit data-moz-translations-id=81><font style=vertical-align:inherit data-moz-translations-id=82>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=83>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=84><font style=vertical-align:inherit data-moz-translations-id=85><font style=vertical-align:inherit data-moz-translations-id=86>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=87><font style=vertical-align:inherit data-moz-translations-id=88><font style=vertical-align:inherit data-moz-translations-id=89>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=90>
|
|||
|
|
<mo data-moz-translations-id=91><font style=vertical-align:inherit data-moz-translations-id=92><font style=vertical-align:inherit data-moz-translations-id=93>
|
|||
|
|
[
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=94>
|
|||
|
|
<mn data-moz-translations-id=95><font style=vertical-align:inherit data-moz-translations-id=96><font style=vertical-align:inherit data-moz-translations-id=97>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=98>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=99>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=100><font style=vertical-align:inherit data-moz-translations-id=101><font style=vertical-align:inherit data-moz-translations-id=102>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=103><font style=vertical-align:inherit data-moz-translations-id=104><font style=vertical-align:inherit data-moz-translations-id=105>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=106><font style=vertical-align:inherit data-moz-translations-id=107><font style=vertical-align:inherit data-moz-translations-id=108>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=109>
|
|||
|
|
<mfrac data-moz-translations-id=110>
|
|||
|
|
<mrow data-moz-translations-id=111>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=112><font style=vertical-align:inherit data-moz-translations-id=113><font style=vertical-align:inherit data-moz-translations-id=114>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=115>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=116>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=117><font style=vertical-align:inherit data-moz-translations-id=118><font style=vertical-align:inherit data-moz-translations-id=119>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=120>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=121><font style=vertical-align:inherit data-moz-translations-id=122><font style=vertical-align:inherit data-moz-translations-id=123>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=124><font style=vertical-align:inherit data-moz-translations-id=125><font style=vertical-align:inherit data-moz-translations-id=126>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=127><font style=vertical-align:inherit data-moz-translations-id=128><font style=vertical-align:inherit data-moz-translations-id=129>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=130><font style=vertical-align:inherit data-moz-translations-id=131><font style=vertical-align:inherit data-moz-translations-id=132>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=133>
|
|||
|
|
<mfrac data-moz-translations-id=134>
|
|||
|
|
<mrow data-moz-translations-id=135>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=136><font style=vertical-align:inherit data-moz-translations-id=137><font style=vertical-align:inherit data-moz-translations-id=138>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=139>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=140>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=141><font style=vertical-align:inherit data-moz-translations-id=142><font style=vertical-align:inherit data-moz-translations-id=143>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=144>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=145><font style=vertical-align:inherit data-moz-translations-id=146><font style=vertical-align:inherit data-moz-translations-id=147>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=148><font style=vertical-align:inherit data-moz-translations-id=149><font style=vertical-align:inherit data-moz-translations-id=150>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=151><font style=vertical-align:inherit data-moz-translations-id=152><font style=vertical-align:inherit data-moz-translations-id=153>
|
|||
|
|
]
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=154><font style=vertical-align:inherit data-moz-translations-id=155><font style=vertical-align:inherit data-moz-translations-id=156>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=157><font style=vertical-align:inherit data-moz-translations-id=158><font style=vertical-align:inherit data-moz-translations-id=159>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=160><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial P}{\partial x}}+A\left(-v{\frac {\partial {\mathfrak {S}}}{\partial x}}\varrho ^{ 2}+{\frac {\partial \psi }{\partial x}}\left[3{\mathfrak {S}}+x{\frac {\partial {\mathfrak {S}}}{\partial z} }+\varrho {\frac {\partial {\mathfrak {S}}}{\partial \varrho }}\right]\right).}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjU1LjY3MmV4IiBoZWlnaHQ9IjYuMTc2ZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTIuNTA1ZXg7IiB2aWV3Qm94PSIwIC0xNTgwLjcgMjM5NjkuNyAyNjU5LjEiIHJvbGU9ImltZyIgZm9jdXNhYmxlPSJmYWxzZSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiBhcmlhLWxhYmVsbGVkYnk9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPgo8dGl0bGUgaWQ9Ik1hdGhKYXgtU1ZHLTEtVGl0bGUiPntcZGlzcGxheXN0eWxlIDA9e1xmcmFjIHtccGFydGlhbCBQfXtccGFydGlhbCB4fX0rQVxsZWZ0KC12e1xmcmFjIHtccGFydGlhbCB7XG1hdGhmcmFrIHtTfX19e1xwYXJ0aWFsIHh9fVx2YXJyaG8gXnsyfSt7XGZyYWMge1xwYXJ0aWFsIFxwc2kgfXtccGFydGlhbCB4fX1cbGVmdFsze1xtYXRoZnJhayB7U319K3h7XGZyYWMge1xwYXJ0aWFsIHtcbWF0aGZyYWsge1N9fX17XHBhcnRpYWwgen19K1x2YXJyaG8ge1xmcmFjIHtccGFydGlhbCB7XG1hdGhmcmFrIHtTfX19e1xwYXJ0aWFsIFx2YXJyaG8gfX1ccmlnaHRdXHJpZ2h0KS59PC90aXRsZT4KPGRlZnMgYXJpYS1oaWRkZW49InRydWUiPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tMzAiIGQ9Ik05NiA1ODVRMTUyIDY2NiAyNDkgNjY2UTI5NyA2NjYgMzQ1IDY0MFQ0MjMgNTQ4UTQ2MCA0NjUgNDYwIDMyMFE0NjAgMTY1IDQxNyA4M1EzOTcgNDEgMzYyIDE2VDMwMSAtMTVUMjUwIC0yMlEyMjQgLTIyIDE5OCAtMTZUMTM3IDE2VDgyIDgzUTM5IDE2NSAzOSAzMjBRMzkgNDk0IDk2IDU4NVpNMzIxIDU5N1EyOTEgNjI5IDI1MCA2MjlRMjA4IDYyOSAxNzggNTk3UTE1MyA1NzEgMTQ1IDUyNVQxMzcgMzMzUTEzNyAxNzUgMTQ1IDEyNVQxODEgNDZRMjA5IDE2IDI1MCAxNlEyOTAgMTYgMzE4IDQ2UTM0NyA3NiAzNTQgMTMwVDM2MiAzMzNRMzYyIDQ3OCAzNTQgNTI0VDMyMSA1OTdaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0zRCIgZD0iTTU2IDM0N1E1NiAzNjAgNzAgMzY3SDcwN1E3MjIgMzU5IDcyMiAzNDdRNzIyIDMzNiA3MDggMzI4TDM5MCAzMjdINzJRNTYgMzMyIDU2IDM0N1pNNTYgMTUzUTU2IDE2OCA3MiAxNzNINzA4UTcyMiAxNjMgNzIyIDE1M1E3MjIgMTQwIDcwNyAxMzNINzBRNTYgMTQwIDU2IDE1M1oiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQUlOLTIyMDIiIGQ9Ik0yMDIgNTA4UTE3OSA1MDggMTY5IDUyMFQxNTggNTQ3UTE1OCA1NTcgMTY0IDU3N1QxODUgNjI0VDIzMCA2NzVUMzAxIDcxMEwzMzMgNzE1SDM0NVEzNzggNzE1IDM4NCA3MTRRNDQ3IDcwMyA0ODkgNjYxVDU0OSA1NjhUNTY2IDQ1N1E1NjYgMzYyIDUxOSAyNDBUNDAyIDUzUTMyMSAtMjIgMjIzIC0yMlExMjMgLTIyIDczIDU2UTQyIDEwMiA0MiAxNDhWMTU5UTQyIDI3NiAxMjkgMzcwVDMyMiA0NjVRMzgzIDQ2NSA0MTQgNDM0VDQ1NSAzNjdMNDU4IDM3OFE0NzggNDYxIDQ3OCA1MTVRNDc4IDYwMyA0MzcgNjM5VDM0NCA2NzZRMjY2IDY3NiAyMjMgNjEyUTI2NCA2MDYgMjY0IDU3MlEyNjQgNTQ3IDI0NiA1MjhUMjAyIDUwOFpNNDMwIDMwNlE0MzAgMzcyIDQwMSA0MDBUMzMzIDQyOFEyNzAgNDI4IDIyMiAzODJRMTk3IDM1NCAxODMgMzIzVDE1MCAyMjFRMTMyIDE0OSAxMzIgMTE2UTEzMiAyMSAyMzIgMjFRMjQ0IDIxIDI1MCAyMlEzMjcgMzUgMzc0IDExMlEzODkgMTM3IDQwOSAxOTZUNDMwIDMwNloiPjwvcGF0aD4KPHBhdGggc3Ryb2tlLXdpZHRoPSIxIiBpZD0iRTEtTUpNQVRISS01MCIgZD0iTTI4NyA2MjhRMjg3IDYzNSAyMzAgNjM3UTIwNiA2MzcgMTk5IDYzOFQxOTIgNjQ4UTE5MiA2NDkgMTk0IDY1OVEyMDAgNjc5IDIwMyA2ODFUMzk3IDY4M1E1ODcgNjgyIDYwMCA2ODBRNjY0IDY2OSA3MDcgNjMxVDc1MSA1MzBRNzUxIDQ1MyA2ODUgMzg5UTYxNiAzMjEgNTA3IDMwM1E1MDAgMzAyIDQwMiAzMDFIMzA3TDI3NyAxODJRMjQ3IDY2IDI0NyA1OVEyNDcgNTUgMjQ4IDU0VDI1NSA1MFQyNzIgNDhUMzA1IDQ2SDMzNlEzNDIgMzcgMzQyIDM1UTM0MiAxOSAzMzUgNVEzMzAgMCAzMTkgMFEzMTYgMCAyODIgMVQxODIgMlExMjAgMiA4NyAyVDUxIDFRMzMgMSAzMyAxMVEzMyAxMyAzNiAyNVE0MCA0MSA0NCA0M1Q2NyA0NlE5NCA0NiAxMjcgNDlRMTQxIDUyIDE0NiA2MVExNDkgNjUgMjE4IDMzOVQyODcgNjI4Wk02NDUgNTU0UTY0NSA1NjcgNjQzIDU3NVQ2MzQgNTk3VDYwOSA2MTlUNTYwIDYzNVE1NTMgNjM2IDQ4MCA2MzdRNDYzIDYzNyA0NDUgNjM3VDQxNiA2MzZUNDA0IDYzNlEzOTEgNjM1IDM4NiA2MjdRMzg0IDYyMSAzNjcgNTUwVDMzMiA0MTJUMzE0IDM0NFEzMTQgMzQyIDM5NSAzNDJINDA3SDQzMFE1NDIgMzQyIDU5MCAzOTJRNjE3IDQxOSA2MzEgNDcxVDY0NSA1NTRaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFUSEktNzgiIGQ9Ik01MiAyODlRNTkgMzMxIDEwNiAzODZUMjIyIDQ0MlEyNTcgNDQyIDI4NiA0MjRUMzI5IDM3OVEzNzEgNDQyIDQzMCA0NDJRNDY3IDQ0MiA0OTQgNDIwVDUyMiAzNjFRNTIyIDMzMiA1MDggMzE0VDQ4MSAyOTJUNDU4IDI4OFE0MzkgMjg4IDQyNyAyOTlUNDE1IDMyOFE0MTUgMzc0IDQ2NSAzOTFRNDU0IDQwNCA0MjUgNDA0UTQxMiA0MDQgNDA2IDQwMlEzNjggMzg2IDM1MCAzMzZRMjkwIDExNSAyOTAgNzhRMjkwIDUwIDMwNiAzOFQzNDEgMjZRMzc4IDI2IDQxNCA1OVQ0NjMgMTQwUTQ2NiAxNTAgNDY5IDE1MVQ0ODUgMTUzSDQ4OVE1MDQgMTUzIDUwNCAxNDVRNTA0IDE0NCA1MDIgMTM0UTQ4NiA3NyA0NDAgMzNUMzMzIC0xMVEyNjMgLTExIDIyNyA1MlExODYgLTEwIDEzMyAtMTBIMTI3UTc4IC0xMCA1NyAxNlQzNSA3MVEzNSAxMDMgNTQgMTIzVDk5IDE0M1ExNDIgMTQzIDE0MiAxMDFRMTQyIDgxIDEzMCA2NlQxMDcgNDZUOTQgNDFMOTEgNDBROTEgMzkgOTcgMzZUMTEzIDI5VDEzMiAyNlExNjggMjYgMTk0IDcxUTIwMyA4NyAyMTcgMTM5
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table><span> <span class=pagenum id=vi title="Page:Translatoric movement of light ether.djvu/6" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>[</font></font> <b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/6 title="Page:Translatoric movement of light ether.djvu/6" data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>vi</font></font></a></b> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>]</font></font></span></span> </span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>We name</font></font><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {U}}}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
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|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
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|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {U}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;margin-left:-0.057ex;width:1.603ex;height:2.176ex alt="{\displaystyle {\mathfrak {U}}}" data-moz-translations-id=11></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>the size</font>
|
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|
|
</font><center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 3{\mathfrak {S}}+x{\frac {\partial {\mathfrak {S}}}{\partial x}}+\varrho {\frac {\partial {\mathfrak {S}}}{\partial \varrho }},}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
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<mn data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
3
|
|||
|
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</font></font></mn>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
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<mi mathvariant=fraktur data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12><font style=vertical-align:inherit data-moz-translations-id=13>
|
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|
|
S
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
|
</mrow>
|
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|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16>
|
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|
|
+
|
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|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit data-moz-translations-id=18><font style=vertical-align:inherit data-moz-translations-id=19>
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|
x
|
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|
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</font></font></mi>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
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<mfrac data-moz-translations-id=21>
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<mrow data-moz-translations-id=22>
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<mi mathvariant=normal data-moz-translations-id=23><font style=vertical-align:inherit data-moz-translations-id=24><font style=vertical-align:inherit data-moz-translations-id=25>
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∂</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
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<mi mathvariant=fraktur data-moz-translations-id=28><font style=vertical-align:inherit data-moz-translations-id=29><font style=vertical-align:inherit data-moz-translations-id=30>
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S
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</font></font></mi>
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</mrow>
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</mrow>
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</mrow>
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<mrow data-moz-translations-id=31>
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<mi mathvariant=normal data-moz-translations-id=32><font style=vertical-align:inherit data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=35><font style=vertical-align:inherit data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37>
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x
|
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</font></font></mi>
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</mrow>
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</mfrac>
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</mrow>
|
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<mo data-moz-translations-id=38><font style=vertical-align:inherit data-moz-translations-id=39><font style=vertical-align:inherit data-moz-translations-id=40>
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+
|
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|
|
</font></font></mo>
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<mi data-moz-translations-id=41><font style=vertical-align:inherit data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43>
|
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|
ϱ</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
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<mfrac data-moz-translations-id=45>
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<mrow data-moz-translations-id=46>
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<mi mathvariant=normal data-moz-translations-id=47><font style=vertical-align:inherit data-moz-translations-id=48><font style=vertical-align:inherit data-moz-translations-id=49>
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|
|
∂</font></font>
|
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|
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</mi>
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
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|
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<mi mathvariant=fraktur data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54>
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|
S
|
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|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=55>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=56><font style=vertical-align:inherit data-moz-translations-id=57><font style=vertical-align:inherit data-moz-translations-id=58>
|
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|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit data-moz-translations-id=60><font style=vertical-align:inherit data-moz-translations-id=61>
|
|||
|
|
ϱ</font></font>
|
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|
|
</mi>
|
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</mrow>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=62><font style=vertical-align:inherit data-moz-translations-id=63><font style=vertical-align:inherit data-moz-translations-id=64>
|
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|
|
,
|
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|
|
</font></font></mo>
|
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|
|
</mstyle>
|
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|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 3{\mathfrak {S}}+x{\frac {\partial {\mathfrak {S}}}{\partial x}}+\varrho {\frac {\partial {\mathfrak {S}}} {\partial \varrho }},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>This results in the elimination of</font></font> <i data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>P</font></font></i></p>
|
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|
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<table width=100%>
|
|||
|
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<tbody>
|
|||
|
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<tr>
|
|||
|
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<td valign=center style=text-align:left width=5%><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>(3)</font></font></td>
|
|||
|
|
<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 0=v\varrho {\frac {\partial {\mathfrak {U}}}{\partial x}}+{\frac {\partial \psi }{\partial x}}{\frac {\partial {\mathfrak {U}}}{\partial \varrho }}-{\frac {\partial \psi }{\partial \varrho }}{\frac {\partial {\mathfrak {U}}}{\partial x}}.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit data-moz-translations-id=16><font style=vertical-align:inherit data-moz-translations-id=17>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
|
<mfrac data-moz-translations-id=19>
|
|||
|
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<mrow data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit data-moz-translations-id=22><font style=vertical-align:inherit data-moz-translations-id=23>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=26><font style=vertical-align:inherit data-moz-translations-id=27><font style=vertical-align:inherit data-moz-translations-id=28>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit data-moz-translations-id=31><font style=vertical-align:inherit data-moz-translations-id=32>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit data-moz-translations-id=34><font style=vertical-align:inherit data-moz-translations-id=35>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit data-moz-translations-id=37><font style=vertical-align:inherit data-moz-translations-id=38>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mfrac data-moz-translations-id=40>
|
|||
|
|
<mrow data-moz-translations-id=41>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=42><font style=vertical-align:inherit data-moz-translations-id=43><font style=vertical-align:inherit data-moz-translations-id=44>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit data-moz-translations-id=46><font style=vertical-align:inherit data-moz-translations-id=47>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=48>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=49><font style=vertical-align:inherit data-moz-translations-id=50><font style=vertical-align:inherit data-moz-translations-id=51>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=52><font style=vertical-align:inherit data-moz-translations-id=53><font style=vertical-align:inherit data-moz-translations-id=54>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mfrac data-moz-translations-id=56>
|
|||
|
|
<mrow data-moz-translations-id=57>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=58><font style=vertical-align:inherit data-moz-translations-id=59><font style=vertical-align:inherit data-moz-translations-id=60>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=61>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=62>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=63><font style=vertical-align:inherit data-moz-translations-id=64><font style=vertical-align:inherit data-moz-translations-id=65>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=66>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=67><font style=vertical-align:inherit data-moz-translations-id=68><font style=vertical-align:inherit data-moz-translations-id=69>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit data-moz-translations-id=71><font style=vertical-align:inherit data-moz-translations-id=72>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit data-moz-translations-id=74><font style=vertical-align:inherit data-moz-translations-id=75>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=76>
|
|||
|
|
<mfrac data-moz-translations-id=77>
|
|||
|
|
<mrow data-moz-translations-id=78>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=79><font style=vertical-align:inherit data-moz-translations-id=80><font style=vertical-align:inherit data-moz-translations-id=81>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=82><font style=vertical-align:inherit data-moz-translations-id=83><font style=vertical-align:inherit data-moz-translations-id=84>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=85>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=86><font style=vertical-align:inherit data-moz-translations-id=87><font style=vertical-align:inherit data-moz-translations-id=88>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=89><font style=vertical-align:inherit data-moz-translations-id=90><font style=vertical-align:inherit data-moz-translations-id=91>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=92>
|
|||
|
|
<mfrac data-moz-translations-id=93>
|
|||
|
|
<mrow data-moz-translations-id=94>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=95><font style=vertical-align:inherit data-moz-translations-id=96><font style=vertical-align:inherit data-moz-translations-id=97>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=98>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=99>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=100><font style=vertical-align:inherit data-moz-translations-id=101><font style=vertical-align:inherit data-moz-translations-id=102>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=103>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=104><font style=vertical-align:inherit data-moz-translations-id=105><font style=vertical-align:inherit data-moz-translations-id=106>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=107><font style=vertical-align:inherit data-moz-translations-id=108><font style=vertical-align:inherit data-moz-translations-id=109>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=110><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=111><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0=v\varrho {\frac {\partial {\mathfrak {U}}}{\partial x}}+{\frac {\partial \psi }{\partial x}}{\frac {\partial {\mathfrak {U}}}{\partial \varrho }}-{\frac {\partial \psi }{\partial \varrho }}{\frac {\partial {\mathfrak {U}}}{\partial x }}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>If the speed in the ether is to remain finite everywhere, it must</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial \psi }{\partial x}}=0}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mrow data-moz-translations-id=8>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial \psi }{\partial x}}=0}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>be, then we have</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle v\varrho ={\frac {\partial \psi }{\partial \varrho }},\quad v=-\alpha .}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
|
<mfrac data-moz-translations-id=10>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mspace width=1em data-moz-translations-id=18></mspace>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle v\varrho ={\frac {\partial \psi }{\partial \varrho }},\quad v=-\alpha .}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>So the ether flows with respect to the coordinate system moving with the speed</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>v</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>in the direction</font> </font><i data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>x x</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>at the same time as the charge with the same speed in the opposite direction, i.e. it rests with respect to a resting coordinate system. This result is remarkable because it shows that the movement of electric quanta is no reason for a movement of the ether, as</font> </font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Helmholtz</font></font></span><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>assumes.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>On the other hand, movements can occur if the aether has an inertia other than zero. I give the calculation for this case because it gives an idea of the magnitude of the density that would have to be assigned to the aether in a given case. Then, in addition to the terms of equations (1), there are also the components of the accelerations</font></font></p>
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<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle s{\frac {d\alpha }{dt}},\quad s{\frac {d\beta }{dt}},\quad s{\frac {d\gamma }{dt}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
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</font></font></mi>
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<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
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α</font></font>
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d
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</font></font></mi>
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<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
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,
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</font></font></mi>
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<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
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β</font></font>
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,
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d
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<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
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γ</font></font>
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<annotation encoding=application/x-tex data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle s{\frac {d\alpha }{dt}},\quad s{\frac {d\beta }{dt}},\quad s{\frac {d\gamma }{dt}}}
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</font></font></annotation>
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</semantics>
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|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>to add, where</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>s</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>denotes the density of the ether and</font></font></p>
|
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|
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<table width=100%>
|
|||
|
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<tbody>
|
|||
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|
<tr>
|
|||
|
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<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{l}{\frac {d\alpha }{dt}}={\frac {\partial \alpha }{\partial t}}+\alpha {\frac {d\alpha }{dx}}+\beta {\frac {\partial \alpha }{\partial y}}+\gamma {\frac {\partial \alpha }{\partial z}},\\\\{\frac {d\beta }{dt}}={\frac {\partial \beta }{\partial t}}+\alpha {\frac {d\beta }{dx}}+\beta {\frac {\partial \beta }{\partial y}}+\gamma {\frac {\partial \beta }{\partial z}},\\\\{\frac {d\gamma }{dt}}={\frac {\partial \gamma }{\partial t}}+\alpha {\frac {d\gamma }{dx}}+\beta {\frac {\partial \gamma }{\partial y}}+\gamma {\frac {\partial \gamma }{\partial z}}\end{array}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
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<mtable columnalign=left rowspacing=4pt columnspacing=1em data-moz-translations-id=7>
|
|||
|
|
<mtr data-moz-translations-id=8>
|
|||
|
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<mtd data-moz-translations-id=9>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
|
<mfrac data-moz-translations-id=11>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
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<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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α</font></font>
|
|||
|
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</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
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<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
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|
d
|
|||
|
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</font></font></mi>
|
|||
|
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<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
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</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
|||
|
|
<mfrac data-moz-translations-id=30>
|
|||
|
|
<mrow data-moz-translations-id=31>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=34>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mfrac data-moz-translations-id=40>
|
|||
|
|
<mrow data-moz-translations-id=41>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=44>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
y
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mfrac data-moz-translations-id=50>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=54>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=58>
|
|||
|
|
<mtd data-moz-translations-id=59></mtd>
|
|||
|
|
</mtr>
|
|||
|
|
<mtr data-moz-translations-id=60>
|
|||
|
|
<mtd data-moz-translations-id=61>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=62>
|
|||
|
|
<mfrac data-moz-translations-id=63>
|
|||
|
|
<mrow data-moz-translations-id=64>
|
|||
|
|
<mi data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=67>
|
|||
|
|
<mi data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=71>
|
|||
|
|
<mfrac data-moz-translations-id=72>
|
|||
|
|
<mrow data-moz-translations-id=73>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=74><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
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|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=76>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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t
|
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|
|
</font></font></mi>
|
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|
|
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|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
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|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
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|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=81>
|
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|
|
<mfrac data-moz-translations-id=82>
|
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<mrow data-moz-translations-id=83>
|
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|
<mi data-moz-translations-id=84><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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d
|
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|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=85><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
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|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=86>
|
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<mi data-moz-translations-id=87><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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d
|
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</font></font></mi>
|
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|
|
<mi data-moz-translations-id=88><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
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|
|
</font></font></mi>
|
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|
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|
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|
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|
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+
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</font></font></mo>
|
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|
|
<mi data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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β</font></font>
|
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|
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</mi>
|
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|
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|
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∂</font></font>
|
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|
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</mi>
|
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|
<mi data-moz-translations-id=95><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
β</font></font>
|
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|
|
</mi>
|
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</mrow>
|
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|
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<mi mathvariant=normal data-moz-translations-id=97><font style=vertical-align:inherit><font style=vertical-align:inherit>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=98><font style=vertical-align:inherit><font style=vertical-align:inherit>
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y
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</font></font></mi>
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+
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</font></font></mo>
|
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|
<mi data-moz-translations-id=100><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
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γ</font></font>
|
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|
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</mi>
|
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<mfrac data-moz-translations-id=102>
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<mrow data-moz-translations-id=103>
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<mi mathvariant=normal data-moz-translations-id=104><font style=vertical-align:inherit><font style=vertical-align:inherit>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=105><font style=vertical-align:inherit><font style=vertical-align:inherit>
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β</font></font>
|
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|
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</mi>
|
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</mrow>
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∂</font></font>
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</mi>
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<mi data-moz-translations-id=108><font style=vertical-align:inherit><font style=vertical-align:inherit>
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e.g
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,
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<mi data-moz-translations-id=117><font style=vertical-align:inherit><font style=vertical-align:inherit>
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d
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|
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<mi data-moz-translations-id=118><font style=vertical-align:inherit><font style=vertical-align:inherit>
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γ</font></font>
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</mi>
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</mrow>
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<mrow data-moz-translations-id=119>
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<mi data-moz-translations-id=120><font style=vertical-align:inherit><font style=vertical-align:inherit>
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d
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t
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<mo data-moz-translations-id=122><font style=vertical-align:inherit><font style=vertical-align:inherit>
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=
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</font></font></mo>
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<mi mathvariant=normal data-moz-translations-id=126><font style=vertical-align:inherit><font style=vertical-align:inherit>
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∂</font></font>
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=127><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
γ</font></font>
|
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|
|
</mi>
|
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|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=128>
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<mi mathvariant=normal data-moz-translations-id=129><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
∂</font></font>
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|
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</mi>
|
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|
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<mi data-moz-translations-id=130><font style=vertical-align:inherit><font style=vertical-align:inherit>
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t
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|
<mo data-moz-translations-id=131><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
+
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|
|
</font></font></mo>
|
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|
|
<mi data-moz-translations-id=132><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
α</font></font>
|
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|
|
</mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=133>
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|
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<mfrac data-moz-translations-id=134>
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|
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<mrow data-moz-translations-id=135>
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<mi data-moz-translations-id=136><font style=vertical-align:inherit><font style=vertical-align:inherit>
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d
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|
|
</font></font></mi>
|
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|
|
<mi data-moz-translations-id=137><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
γ</font></font>
|
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|
|
</mi>
|
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|
|
</mrow>
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|
|
<mrow data-moz-translations-id=138>
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<mi data-moz-translations-id=139><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
d
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</font></font></mi>
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|
|
<mi data-moz-translations-id=140><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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x
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|
|
</font></font></mi>
|
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|
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</mrow>
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|
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</mfrac>
|
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|
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</mrow>
|
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|
|
<mo data-moz-translations-id=141><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
+
|
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|
|
</font></font></mo>
|
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|
|
<mi data-moz-translations-id=142><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
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|
|
</mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=143>
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|
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<mfrac data-moz-translations-id=144>
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|
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<mrow data-moz-translations-id=145>
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|
|
<mi mathvariant=normal data-moz-translations-id=146><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
∂</font></font>
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=147><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
γ</font></font>
|
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|
|
</mi>
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|
|
</mrow>
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|
|
<mrow data-moz-translations-id=148>
|
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|
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<mi mathvariant=normal data-moz-translations-id=149><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
∂</font></font>
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=150><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
y
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|
|
</font></font></mi>
|
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|
|
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|
|
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</mrow>
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|
|
<mo data-moz-translations-id=151><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
+
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|
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</font></font></mo>
|
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|
|
<mi data-moz-translations-id=152><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
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|
|
</mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=153>
|
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|
|
<mfrac data-moz-translations-id=154>
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|
|
<mrow data-moz-translations-id=155>
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|
|
<mi mathvariant=normal data-moz-translations-id=156><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
|
∂</font></font>
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=157><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
γ</font></font>
|
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|
|
</mi>
|
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|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=158>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=159><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=160><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
e.g
|
|||
|
|
</font></font></mi>
|
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|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=161><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{l}{\frac {d\alpha }{dt}}={\frac {\partial \alpha }{\partial t}}+\alpha {\frac {d\alpha }{dx}}+\beta {\frac {\partial \alpha }{\partial y}}+\gamma {\frac {\partial \alpha }{\partial z}},\\\\{\frac { d\beta }{dt}}={\frac {\partial \beta }{\partial t}}+\alpha {\frac {d\beta }{dx}}+\beta {\frac {\partial \beta }{\partial y}}+\gamma {\frac {\partial \beta }{\partial z}},\\\\{\frac {d\gamma }{dt}}={\frac {\partial \ gamma }{\partial t}}+\alpha {\frac {d\gamma }{dx}}+\beta {\frac {\partial \gamma }{\partial y}}+\gamma {\frac {\partial \gamma }{\partial z}}\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><span data-moz-translations-id=0><span class=pagenum id=vii title="Page:Translatoric movement of light ether.djvu/7" data-moz-translations-id=1><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=2><b data-moz-translations-id=3><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/7 title="Page:Translatoric movement of light ether.djvu/7" data-moz-translations-id=4></a></b></span></span></span><font style=vertical-align:inherit></font></p>
|
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<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial \alpha }{\partial t}}={\frac {\partial \beta }{\partial t}}={\frac {\partial \gamma }{\partial t}}=0.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
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<mfrac data-moz-translations-id=7>
|
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<mrow data-moz-translations-id=8>
|
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<mi mathvariant=normal data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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α</font></font>
|
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</mi>
|
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</mrow>
|
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<mrow data-moz-translations-id=11>
|
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<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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t
|
|||
|
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</font></font></mi>
|
|||
|
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</mrow>
|
|||
|
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</mfrac>
|
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|
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</mrow>
|
|||
|
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<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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=
|
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</font></font></mo>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
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|
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<mfrac data-moz-translations-id=16>
|
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<mrow data-moz-translations-id=17>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
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<mfrac data-moz-translations-id=25>
|
|||
|
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<mrow data-moz-translations-id=26>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial \alpha }{\partial t}}={\frac {\partial \beta }{\partial t}}={\frac {\partial \gamma }{\partial t}} =0.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Let's set the values of</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \alpha ,\beta ,\gamma }" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
β</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \alpha ,\beta ,\gamma }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:6.15ex;height:2.676ex alt="{\displaystyle \alpha ,\beta ,\gamma }" data-moz-translations-id=12></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>one, the eliminat
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {1}{A}}{\frac {\partial \psi }{\partial x}}{\frac {\partial }{\partial \varrho }}\left[{\frac {1}{\varrho ^{2}}}\left({\frac {\partial ^{2}\psi }{\partial \varrho ^{2}}}-{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}+{\frac {\partial ^{2}\psi }{\partial x^{2}}}\right)\right]}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mfrac data-moz-translations-id=6>
|
|||
|
|
<mn data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
|
<mfrac data-moz-translations-id=10>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mfrac data-moz-translations-id=18>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=23>
|
|||
|
|
<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
[
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mfrac data-moz-translations-id=27>
|
|||
|
|
<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=29>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=33>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=35>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=36>
|
|||
|
|
<mfrac data-moz-translations-id=37>
|
|||
|
|
<mrow data-moz-translations-id=38>
|
|||
|
|
<msup data-moz-translations-id=39>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
|
|||
|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=44>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=46>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=48>
|
|||
|
|
<mn data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
|
<mfrac data-moz-translations-id=52>
|
|||
|
|
<mn data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mfrac data-moz-translations-id=56>
|
|||
|
|
<mrow data-moz-translations-id=57>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=60>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=64>
|
|||
|
|
<mfrac data-moz-translations-id=65>
|
|||
|
|
<mrow data-moz-translations-id=66>
|
|||
|
|
<msup data-moz-translations-id=67>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=69>
|
|||
|
|
<mn data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=72>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=74>
|
|||
|
|
<mi data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=76>
|
|||
|
|
<mn data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
]
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {1}{A}}{\frac {\partial \psi }{\partial x}}{\frac {\partial }{\partial \varrho }}\left[{\frac {1 }{\varrho ^{2}}}\left({\frac {\partial ^{2}\psi }{\partial \varrho ^{2}}}-{\frac {1}{\varrho }}{ \frac {\partial \psi }{\partial \varrho }}+{\frac {\partial ^{2}\psi }{\partial x^{2}}}\right)\right]}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mfrac data-moz-translations-id=8>
|
|||
|
|
<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mfrac data-moz-translations-id=12>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
[
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mfrac data-moz-translations-id=29>
|
|||
|
|
<mn data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=31>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mn data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=35>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=37>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mfrac data-moz-translations-id=39>
|
|||
|
|
<mrow data-moz-translations-id=40>
|
|||
|
|
<msup data-moz-translations-id=41>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=43>
|
|||
|
|
<mn data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=46>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=48>
|
|||
|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mn data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=53>
|
|||
|
|
<mfrac data-moz-translations-id=54>
|
|||
|
|
<mn data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=57>
|
|||
|
|
<mfrac data-moz-translations-id=58>
|
|||
|
|
<mrow data-moz-translations-id=59>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=62>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=66>
|
|||
|
|
<mfrac data-moz-translations-id=67>
|
|||
|
|
<mrow data-moz-translations-id=68>
|
|||
|
|
<msup data-moz-translations-id=69>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=71>
|
|||
|
|
<mn data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=74>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=76>
|
|||
|
|
<mi data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=78>
|
|||
|
|
<mn data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
]
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=82><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle -{\frac {1}{A}}{\frac {\partial \psi }{\partial \varrho }}{\frac {\partial }{\partial x}}\left[{\frac { 1}{\varrho ^{2}}}\left({\frac {\partial ^{2}\psi }{\partial \varrho ^{2}}}-{\frac {1}{\varrho }} {\frac {\partial \psi }{\partial \varrho }}+{\frac {\partial ^{2}\psi }{\partial x^{2}}}\right)\right]}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mfrac data-moz-translations-id=8>
|
|||
|
|
<mrow data-moz-translations-id=9>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mfrac data-moz-translations-id=14>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=20>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=26>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mfrac data-moz-translations-id=28>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=32>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=35>
|
|||
|
|
<mfrac data-moz-translations-id=36>
|
|||
|
|
<mrow data-moz-translations-id=37>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=40>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=42>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
|||
|
|
<mfrac data-moz-translations-id=47>
|
|||
|
|
<mrow data-moz-translations-id=48>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=54>
|
|||
|
|
<mfrac data-moz-translations-id=55>
|
|||
|
|
<mrow data-moz-translations-id=56>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=58>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
|||
|
|
<mfrac data-moz-translations-id=66>
|
|||
|
|
<mn data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0.
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle +{\frac {v\varrho }{s}}{\frac {\partial {\mathfrak {U}}}{\partial x}}+\left({\frac {\partial \psi }{ \partial x}}{\frac {\partial {\mathfrak {U}}}{\partial \varrho }}-{\frac {\partial \psi }{\partial \varrho }}{\frac {\partial { \mathfrak {U}}}{\partial x}}\right){\frac {1}{s}}=0.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>This equation is satisfied if</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\begin{array}{lr}{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}=&v+{\frac {1}{\varrho }}{\frac {\partial \psi _{1}}{\partial \varrho }},\\\\{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial x}}=&{\frac {1}{\varrho }}{\frac {\partial \psi _{1}}{\partial x}},\end{array}}}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=5>
|
|||
|
|
<mtable columnalign="left right" rowspacing=4pt columnspacing=1em data-moz-translations-id=6>
|
|||
|
|
<mtr data-moz-translations-id=7>
|
|||
|
|
<mtd data-moz-translations-id=8>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=9>
|
|||
|
|
<mfrac data-moz-translations-id=10>
|
|||
|
|
<mn data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mfrac data-moz-translations-id=14>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=22>
|
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|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
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|
|
</font></font></mi>
|
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|
|
<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
+
|
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|
|
</font></font></mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
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|
|
<mfrac data-moz-translations-id=26>
|
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|
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<mn data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
1
|
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|
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</font></font></mn>
|
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|
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<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
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</mi>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
|
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|
|
<mfrac data-moz-translations-id=30>
|
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|
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<mrow data-moz-translations-id=31>
|
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|
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<mi mathvariant=normal data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
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|
|
</mi>
|
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|
|
<msub data-moz-translations-id=33>
|
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|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ψ</font></font>
|
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|
|
</mi>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=35>
|
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|
|
<mn data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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1
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
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|
|
</msub>
|
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|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=37>
|
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|
|
<mi mathvariant=normal data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
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|
|
</mi>
|
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|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
</mrow>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
,
|
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|
|
</font></font></mo>
|
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|
|
</mtd>
|
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|
|
</mtr>
|
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|
|
<mtr data-moz-translations-id=41>
|
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|
|
<mtd data-moz-translations-id=42></mtd>
|
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|
|
</mtr>
|
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|
|
<mtr data-moz-translations-id=43>
|
|||
|
|
<mtd data-moz-translations-id=44>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
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|
|
<mfrac data-moz-translations-id=46>
|
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|
|
<mn data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
1
|
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|
|
</font></font></mn>
|
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|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mfrac data-moz-translations-id=50>
|
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|
|
<mrow data-moz-translations-id=51>
|
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|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
|||
|
|
</mi>
|
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|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ψ</font></font>
|
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|
|
</mi>
|
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|
|
</mrow>
|
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|
|
<mrow data-moz-translations-id=54>
|
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|
|
<mi mathvariant=normal data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
∂</font></font>
|
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|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
x
|
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|
|
</font></font></mi>
|
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|
|
</mrow>
|
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|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
<mtd data-moz-translations-id=58>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mfrac data-moz-translations-id=60>
|
|||
|
|
<mn data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
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|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
</mfrac>
|
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|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mfrac data-moz-translations-id=64>
|
|||
|
|
<mrow data-moz-translations-id=65>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msub data-moz-translations-id=67>
|
|||
|
|
<mi data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=69>
|
|||
|
|
<mn data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
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|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=71>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=74><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mtd>
|
|||
|
|
</mtr>
|
|||
|
|
</mtable>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\begin{array}{lr}{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial \varrho }}=&v+{\frac {1}{\varrho }}{\frac {\partial \psi _{1}}{\partial \varrho }},\\\\{\frac {1}{\varrho }}{\frac {\partial \psi }{\partial x}}=&{\frac {1}{\varrho }}{\frac {\partial \psi _{1}}{\partial x}},\end{array}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mn data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=9>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=16>
|
|||
|
|
<mfrac data-moz-translations-id=17>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<msup data-moz-translations-id=19>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msub data-moz-translations-id=23>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=29>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mfrac data-moz-translations-id=35>
|
|||
|
|
<mn data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mfrac data-moz-translations-id=39>
|
|||
|
|
<mrow data-moz-translations-id=40>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msub data-moz-translations-id=42>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
|||
|
|
<mn data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=46>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mfrac data-moz-translations-id=51>
|
|||
|
|
<mrow data-moz-translations-id=52>
|
|||
|
|
<msup data-moz-translations-id=53>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msub data-moz-translations-id=57>
|
|||
|
|
<mi data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mn data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=63>
|
|||
|
|
<mi data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
|||
|
|
<mn data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=70>
|
|||
|
|
<mfrac data-moz-translations-id=71>
|
|||
|
|
<mrow data-moz-translations-id=72>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=73>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=74>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=76><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {1}{\varrho ^{2}}}\left({\frac {\partial ^{2}\psi _{1}}{\partial \varrho ^{2}}}- {\frac {1}{\varrho }}{\frac {\partial \psi _{1}}{\partial \varrho }}+{\frac {\partial ^{2}\psi _{1}}{ \partial x^{2}}}\right)=-{\frac {{\mathfrak {U}}A}{s}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>is. It is</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {U}}=-{\frac {3A}{\left(x^{2}+\varrho ^{2}\left(1-A^{2}v^{2}\right)\right)^{3}}}.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mfrac data-moz-translations-id=12>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
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</font></font></mn>
|
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<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
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A
|
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</font></font></mi>
|
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</mrow>
|
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<msup data-moz-translations-id=16>
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<mrow data-moz-translations-id=17>
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<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
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(
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</font></font></mo>
|
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<mrow data-moz-translations-id=19>
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<msup data-moz-translations-id=20>
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<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=22>
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<mn data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
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</mrow>
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</msup>
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<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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+
|
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</font></font></mo>
|
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<msup data-moz-translations-id=25>
|
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<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
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<mn data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
|
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</font></font></mn>
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</msup>
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<mrow data-moz-translations-id=29>
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<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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(
|
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</font></font></mo>
|
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<mrow data-moz-translations-id=31>
|
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<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
|
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<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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−</font></font>
|
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</mo>
|
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<msup data-moz-translations-id=34>
|
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<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=36>
|
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<mn data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
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<msup data-moz-translations-id=38>
|
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<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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v
|
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|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=40>
|
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<mn data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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|
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</msup>
|
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</mrow>
|
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<mo data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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)
|
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</font></font></mo>
|
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</mrow>
|
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</mrow>
|
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<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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)
|
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</font></font></mo>
|
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</mrow>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
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<mn data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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3
|
|||
|
|
</font></font></mn>
|
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|
|
</mrow>
|
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|
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</msup>
|
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|
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</mfrac>
|
|||
|
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</mrow>
|
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<mo data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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.
|
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|
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</font></font></mo>
|
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</mstyle>
|
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</mrow>
|
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|
|
<annotation encoding=application/x-tex data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {U}}=-{\frac {3A}{\left(x^{2}+\varrho ^{2}\left(1-A^{2}v^{2}\ right)\right)^{3}}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>To integrate the differential equation, we set</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \psi _{1}=\varrho \varphi .}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<msub data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \psi _{1}=\varrho \varphi .}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Then it will be</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial ^{2}\varphi }{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial \varphi }{\partial \varrho }}-{\frac {1}{\varrho ^{2}}}\varphi +{\frac {\partial ^{2}\varphi }{\partial x^{2}}}=-{\frac {\varrho {\mathfrak {U}}A}{s}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mrow data-moz-translations-id=8>
|
|||
|
|
<msup data-moz-translations-id=9>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=16>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
|
<mn data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mfrac data-moz-translations-id=22>
|
|||
|
|
<mn data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mfrac data-moz-translations-id=26>
|
|||
|
|
<mrow data-moz-translations-id=27>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=30>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mfrac data-moz-translations-id=35>
|
|||
|
|
<mn data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=37>
|
|||
|
|
<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
|||
|
|
<mn data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=43>
|
|||
|
|
<mfrac data-moz-translations-id=44>
|
|||
|
|
<mrow data-moz-translations-id=45>
|
|||
|
|
<msup data-moz-translations-id=46>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=48>
|
|||
|
|
<mn data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=53>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mfrac data-moz-translations-id=60>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=64>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial ^{2}\varphi }{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial \varphi }{\ partial \varrho }}-{\frac {1}{\varrho ^{2}}}\varphi +{\frac {\partial ^{2}\varphi }{\partial x^{2}}}=-{ \frac {\varrho {\mathfrak {U}}A}{s}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
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|
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>We first consider the differential equation</font></font></p>
|
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<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial ^{2}\varphi _{1}}{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial \varphi _{1}}{\partial \varrho }}+{\frac {1}{\varrho ^{2}}}{\frac {\partial ^{2}\varphi _{1}}{\partial \vartheta ^{2}}}+{\frac {\partial ^{2}\varphi _{1}}{\partial x^{2}}}=-{\frac {\varrho {\mathfrak {U}}A}{s}}\sin \vartheta .}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
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<mfrac data-moz-translations-id=7>
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<mrow data-moz-translations-id=8>
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<msup data-moz-translations-id=9>
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<mi mathvariant=normal data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∂</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
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<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
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</mrow>
|
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</msup>
|
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<msub data-moz-translations-id=13>
|
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<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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φ</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
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<mn data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
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</mrow>
|
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</msub>
|
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</mrow>
|
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<mrow data-moz-translations-id=17>
|
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<mi mathvariant=normal data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∂</font></font>
|
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</mi>
|
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|
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<msup data-moz-translations-id=19>
|
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<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
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<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
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</mrow>
|
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</msup>
|
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</mrow>
|
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</mfrac>
|
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</mrow>
|
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<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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+
|
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</font></font></mo>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
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<mfrac data-moz-translations-id=25>
|
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<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
|
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<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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</mfrac>
|
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</mrow>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
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<mfrac data-moz-translations-id=29>
|
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<mrow data-moz-translations-id=30>
|
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<mi mathvariant=normal data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<msub data-moz-translations-id=32>
|
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|
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<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
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φ</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
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<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
|
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</mrow>
|
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</msub>
|
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</mrow>
|
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<mrow data-moz-translations-id=36>
|
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<mi mathvariant=normal data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∂</font></font>
|
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</mi>
|
|||
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<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
|||
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</mi>
|
|||
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</mrow>
|
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</mfrac>
|
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</mrow>
|
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<mo data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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+
|
|||
|
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</font></font></mo>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=40>
|
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<mfrac data-moz-translations-id=41>
|
|||
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<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
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1
|
|||
|
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</font></font></mn>
|
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<msup data-moz-translations-id=43>
|
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<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
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<mn data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
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</mfrac>
|
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</mrow>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
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<mfrac data-moz-translations-id=48>
|
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<mrow data-moz-translations-id=49>
|
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<msup data-moz-translations-id=50>
|
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<mi mathvariant=normal data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=52>
|
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<mn data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
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<msub data-moz-translations-id=54>
|
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<mi data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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φ</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=56>
|
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<mn data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
|
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</mrow>
|
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</msub>
|
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</mrow>
|
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<mrow data-moz-translations-id=58>
|
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<mi mathvariant=normal data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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∂</font></font>
|
|||
|
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</mi>
|
|||
|
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<msup data-moz-translations-id=60>
|
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|
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<mi data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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ϑ</font></font>
|
|||
|
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</mi>
|
|||
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=62>
|
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<mn data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
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2
|
|||
|
|
</font></font></mn>
|
|||
|
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</mrow>
|
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</msup>
|
|||
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</mrow>
|
|||
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</mfrac>
|
|||
|
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</mrow>
|
|||
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<mo data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
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|
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<mfrac data-moz-translations-id=66>
|
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|
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<mrow data-moz-translations-id=67>
|
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<msup data-moz-translations-id=68>
|
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|
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<mi mathvariant=normal data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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∂</font></font>
|
|||
|
|
</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=70>
|
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|
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<mn data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
|||
|
|
</font></font></mn>
|
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</mrow>
|
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</msup>
|
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<msub data-moz-translations-id=72>
|
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|
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<mi data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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φ</font></font>
|
|||
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=74>
|
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<mn data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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|
|
</font></font></mn>
|
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</mrow>
|
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</msub>
|
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|
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</mrow>
|
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<mrow data-moz-translations-id=76>
|
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<mi mathvariant=normal data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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∂</font></font>
|
|||
|
|
</mi>
|
|||
|
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<msup data-moz-translations-id=78>
|
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|
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<mi data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=80>
|
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<mn data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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|
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</msup>
|
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|
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|
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|
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<mo data-moz-translations-id=82><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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=
|
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|
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</font></font></mo>
|
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<mo data-moz-translations-id=83><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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−</font></font>
|
|||
|
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</mo>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=84>
|
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<mfrac data-moz-translations-id=85>
|
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<mrow data-moz-translations-id=86>
|
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<mi data-moz-translations-id=87><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=88>
|
|||
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=89>
|
|||
|
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<mi mathvariant=fraktur data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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U
|
|||
|
|
</font></font></mi>
|
|||
|
|
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|
|||
|
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</mrow>
|
|||
|
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<mi data-moz-translations-id=91><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
|||
|
|
</font></font></mi>
|
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</mrow>
|
|||
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<mi data-moz-translations-id=92><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
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<mi data-moz-translations-id=93><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=94><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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</font></font>
|
|||
|
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</mo>
|
|||
|
|
<mi data-moz-translations-id=95><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
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<mo data-moz-translations-id=96><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
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|
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</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=97><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial ^{2}\varphi _{1}}{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial \ varphi _{1}}{\partial \varrho }}+{\frac {1}{\varrho ^{2}}}{\frac {\partial ^{2}\varphi _{1}}{\partial \ vartheta ^{2}}}+{\frac {\partial ^{2}\varphi _{1}}{\partial x^{2}}}=-{\frac {\varrho {\mathfrak {U}} A}{s}}\sin \vartheta .}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Their integral is</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varphi _{1}={\frac {A}{4\pi s}}\int \int \int {\frac {d\varrho '\ d\vartheta '\ dx'\ \varrho '^{2}\ {\mathfrak {U}}'\sin \vartheta '}{\sqrt {\left(x-x'\right)^{2}+\varrho ^{2}+\varrho '^{2}-2\varrho \varrho '\cos(\vartheta -\vartheta ')}}},}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
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<msub data-moz-translations-id=5>
|
|||
|
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<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
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<mn data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
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<mfrac data-moz-translations-id=11>
|
|||
|
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<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
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<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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4
|
|||
|
|
</font></font></mn>
|
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|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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s
|
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|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∫</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∫</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∫</font></font>
|
|||
|
|
</mo>
|
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|
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|
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<mfrac data-moz-translations-id=21>
|
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<mrow data-moz-translations-id=22>
|
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<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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d
|
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|
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</font></font></mi>
|
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|
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<msup data-moz-translations-id=24>
|
|||
|
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<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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ϱ</font></font>
|
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|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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′
|
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|
|
</font></font></mo>
|
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|
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</msup>
|
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|
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<mtext data-moz-translations-id=27>
|
|||
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|
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|
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</mtext>
|
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|
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<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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|
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|
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<msup data-moz-translations-id=29>
|
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|
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|
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|
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|
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</mi>
|
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|
|
<mo data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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|
|
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|
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|
</msup>
|
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|
|
<mtext data-moz-translations-id=32>
|
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|
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|
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|
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|
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<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
d
|
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|
|
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|
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<msup data-moz-translations-id=34>
|
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<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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|
|
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|
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|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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|
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|
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|
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<mtext data-moz-translations-id=37>
|
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|
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</mtext>
|
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|
|
<msup data-moz-translations-id=38>
|
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|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
ϱ</font></font>
|
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|
|
</mi>
|
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|
|
<mrow data-moz-translations-id=40>
|
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<mo class=MJX-variant data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
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′
|
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|
|
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|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
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|
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<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
2
|
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|
|
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|
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|
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|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
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|
|
<mtext data-moz-translations-id=44>
|
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|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
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|
<mi mathvariant=fraktur data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
U
|
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|
|
</font></font></mi>
|
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|
</mrow>
|
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|
</mrow>
|
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|
|
<mo data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
′
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|
</font></font></mo>
|
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|
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|
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|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=52>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<msqrt data-moz-translations-id=55>
|
|||
|
|
<msup data-moz-translations-id=56>
|
|||
|
|
<mrow data-moz-translations-id=57>
|
|||
|
|
<mo data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=59>
|
|||
|
|
<mi data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=62>
|
|||
|
|
<mi data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=66>
|
|||
|
|
<mn data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=69>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=71>
|
|||
|
|
<mn data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=74>
|
|||
|
|
<mi data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow data-moz-translations-id=76>
|
|||
|
|
<mo class=MJX-variant data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=78>
|
|||
|
|
<mn data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mn data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=82><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=83>
|
|||
|
|
<mi data-moz-translations-id=84><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=85><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=86><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=87><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mo stretchy=false data-moz-translations-id=88><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=89><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=91>
|
|||
|
|
<mi data-moz-translations-id=92><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=93><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<mo stretchy=false data-moz-translations-id=94><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msqrt>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=95><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=96><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varphi _{1}={\frac {A}{4\pi s}}\int \int \int {\frac {d\varrho '\ d\vartheta '\ dx'\ \varrho '^ {2}\ {\mathfrak {U}}'\sin \vartheta '}{\sqrt {\left(xx'\right)^{2}+\varrho ^{2}+\varrho '^{2}- 2\varrho \varrho '\cos(\vartheta -\vartheta ')}}},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mo data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϑ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle =S\sin \vartheta }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
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<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
4
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∫</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mo data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∫</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mo class=MJX-variant data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mn data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=24>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=31>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle S={\frac {A}{4\pi s}}\int \int \varrho '^{2}d\varrho 'dx'{\mathfrak {U}}'R,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mn data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msqrt data-moz-translations-id=11>
|
|||
|
|
<msup data-moz-translations-id=12>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
′
|
|||
|
|
</font></font></mo>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</msqrt>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=22>
|
|||
|
|
<mfrac data-moz-translations-id=23>
|
|||
|
|
<mn data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϰ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
K
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mfrac data-moz-translations-id=32>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϰ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
E
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle R={\frac {2}{\sqrt {\varrho '\varrho }}}\left(\left({\frac {2}{x}}-\varkappa \right)K-{\frac {2}{\varkappa }}E\right),}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table><span> <span class=pagenum id=viii title="Page:Translatoric movement of the Lichtäthers.djvu/8" data-moz-translations-id=0><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[</font> </font><b data-moz-translations-id=2><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/8 title="Page:Translatoric movement of the Lichtäthers.djvu/8" data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>viii</font></font></a></b><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>]</font></font></span></span> </span>
|
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<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varkappa ^{2}={\frac {4\varrho '\varrho }{(z'-z)^{2}+(\varrho +\varrho ')^{2}}},\quad K=\int \limits _{0}^{\frac {\pi }{2}}{\frac {d\varphi }{\sqrt {1-\varkappa ^{2}\sin ^{2}\varphi }}},\quad E=\int \limits _{0}^{\frac {\pi }{2}}{\frac {d\varphi }{\sqrt {1-\varkappa ^{2}\sin ^{3}\varphi }}}.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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<msup data-moz-translations-id=6>
|
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<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϰ</font></font>
|
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</mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
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<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
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<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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=
|
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</font></font></mo>
|
|||
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
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<mfrac data-moz-translations-id=12>
|
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<mrow data-moz-translations-id=13>
|
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<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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4
|
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</font></font></mn>
|
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<msup data-moz-translations-id=15>
|
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<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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′
|
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|
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</font></font></mo>
|
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</msup>
|
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<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
|||
|
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</mi>
|
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|
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</mrow>
|
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<mrow data-moz-translations-id=19>
|
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<mo stretchy=false data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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(
|
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</font></font></mo>
|
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<msup data-moz-translations-id=21>
|
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<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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e.g
|
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</font></font></mi>
|
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<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
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′
|
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</font></font></mo>
|
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</msup>
|
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|
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<mo data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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−</font></font>
|
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</mo>
|
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<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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e.g
|
|||
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</font></font></mi>
|
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|
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<msup data-moz-translations-id=26>
|
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<mo stretchy=false data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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)
|
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|
|
</font></font></mo>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
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<mn data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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2
|
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|
|
</font></font></mn>
|
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|
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</mrow>
|
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</msup>
|
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|
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<mo data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
+
|
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|
|
</font></font></mo>
|
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<mo stretchy=false data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
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(
|
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|
|
</font></font></mo>
|
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<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
+
|
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|
|
</font></font></mo>
|
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<msup data-moz-translations-id=34>
|
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<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
ϱ</font></font>
|
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</mi>
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</font></font></mo>
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)
|
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|
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</font></font></mo>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
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|
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<mn data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
|
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|
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</font></font></mn>
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</mrow>
|
|||
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</msup>
|
|||
|
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</mrow>
|
|||
|
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</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
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|
|
<mspace width=1em data-moz-translations-id=42></mspace>
|
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|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
K
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<munderover data-moz-translations-id=45>
|
|||
|
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<mo data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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∫</font></font>
|
|||
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</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
|||
|
|
<mn data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mfrac data-moz-translations-id=50>
|
|||
|
|
<mi data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mn data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</munderover>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=53>
|
|||
|
|
<mfrac data-moz-translations-id=54>
|
|||
|
|
<mrow data-moz-translations-id=55>
|
|||
|
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<mi data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
d
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<msqrt data-moz-translations-id=58>
|
|||
|
|
<mn data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=61>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϰ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mn data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=65>
|
|||
|
|
<mi data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=67>
|
|||
|
|
<mn data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
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|
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|
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|
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|
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<mo data-moz-translations-id=71><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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,
|
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</font></font></mo>
|
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<mspace width=1em data-moz-translations-id=72></mspace>
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E
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</font></font></mi>
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|
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=
|
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</font></font></mo>
|
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<munderover data-moz-translations-id=75>
|
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<mo data-moz-translations-id=76><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∫</font></font>
|
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</mo>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=77>
|
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<mn data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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0
|
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</font></font></mn>
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=79>
|
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<mfrac data-moz-translations-id=80>
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<mi data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
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</mi>
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<mn data-moz-translations-id=82><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
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|
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|
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<mfrac data-moz-translations-id=84>
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d
|
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</font></font></mi>
|
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φ</font></font>
|
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|
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|
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<mn data-moz-translations-id=89><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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|
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</font></font></mn>
|
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<mo data-moz-translations-id=90><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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−</font></font>
|
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|
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</mo>
|
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<msup data-moz-translations-id=91>
|
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<mi data-moz-translations-id=92><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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ϰ</font></font>
|
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|
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</mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=93>
|
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<mn data-moz-translations-id=94><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
|
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</font></font></mn>
|
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</mrow>
|
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</msup>
|
|||
|
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<msup data-moz-translations-id=95>
|
|||
|
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<mi data-moz-translations-id=96><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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sin
|
|||
|
|
</font></font></mi>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=97>
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<mn data-moz-translations-id=98><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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3
|
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|
|
</font></font></mn>
|
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|
|
</mrow>
|
|||
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|
|||
|
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<mo data-moz-translations-id=99><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=100><font style=vertical-align:inherit><font style=vertical-align:inherit>
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|
φ</font></font>
|
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|
</mi>
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|
</msqrt>
|
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|
</mfrac>
|
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|
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</mrow>
|
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<mo data-moz-translations-id=101><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=102><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varkappa ^{2}={\frac {4\varrho '\varrho }{(z'-z)^{2}+(\varrho +\varrho ')^{2}}},\quad K=\int \limits _{0}^{\frac {\pi }{2}}{\frac {d\varphi }{\sqrt {1-\varkappa ^{2}\sin ^{2}\varphi }}},\quad E=\int \limits _{0}^{\frac {\pi }{2}}{\frac {d\varphi }{\sqrt {1-\varkappa ^{2}\sin ^{3}\varphi }}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Then</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>S</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>satisfies the differential equation</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial ^{2}S}{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial S}{\partial \varrho }}-{\frac {1}{\varrho ^{2}}}S+{\frac {\partial ^{2}S}{\partial x^{2}}}=-{\frac {\varrho {\mathfrak {U}}A}{s}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mrow data-moz-translations-id=8>
|
|||
|
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<msup data-moz-translations-id=9>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
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<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=16>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
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<mn data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mfrac data-moz-translations-id=22>
|
|||
|
|
<mn data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
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<mfrac data-moz-translations-id=26>
|
|||
|
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<mrow data-moz-translations-id=27>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=30>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=34>
|
|||
|
|
<mfrac data-moz-translations-id=35>
|
|||
|
|
<mn data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<msup data-moz-translations-id=37>
|
|||
|
|
<mi data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=39>
|
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|
|
<mn data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=43>
|
|||
|
|
<mfrac data-moz-translations-id=44>
|
|||
|
|
<mrow data-moz-translations-id=45>
|
|||
|
|
<msup data-moz-translations-id=46>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=48>
|
|||
|
|
<mn data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<msup data-moz-translations-id=53>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mfrac data-moz-translations-id=60>
|
|||
|
|
<mrow data-moz-translations-id=61>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=64>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
U
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=66><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=67><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial ^{2}S}{\partial \varrho ^{2}}}+{\frac {1}{\varrho }}{\frac {\partial S}{\partial \ varrho }}-{\frac {1}{\varrho ^{2}}}S+{\frac {\partial ^{2}S}{\partial x^{2}}}=-{\frac {\varrho {\mathfrak {U}}A}{s}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>and so it is</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varphi =S}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
S
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varphi =S}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:6.118ex;height:2.676ex alt="{\displaystyle \varphi =S}" data-moz-translations-id=10></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>These are the same expressions that give the velocities of the circular vortex rings in a liquid, where the</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>x x</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>-axis is the axis of the vortex rings when the rotation speed of the liquid particles is about the circular rotation axis</font></font></p>
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<center>
|
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<span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {3{\mathfrak {A}}\varrho A}{2s\left[x^{2}+\varrho ^{2}\left(1-A^{2}v^{2}\right)\right]^{3}}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
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<mfrac data-moz-translations-id=7>
|
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<mrow data-moz-translations-id=8>
|
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<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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3
|
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</font></font></mn>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
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<mi mathvariant=fraktur data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
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</font></font></mi>
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|
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|
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<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ϱ</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
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</font></font></mi>
|
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|
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<mrow data-moz-translations-id=15>
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<mn data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
|
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</font></font></mn>
|
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<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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s
|
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</font></font></mi>
|
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<msup data-moz-translations-id=18>
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<mrow data-moz-translations-id=19>
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<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
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[
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</font></font></mo>
|
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<mrow data-moz-translations-id=21>
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<msup data-moz-translations-id=22>
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<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
|
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</font></font></mi>
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<mn data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
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<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
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+
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</font></font></mo>
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<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
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ϱ</font></font>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=29>
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<mn data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
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<mrow data-moz-translations-id=31>
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<mo data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
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(
|
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</font></font></mo>
|
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<mrow data-moz-translations-id=33>
|
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<mn data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
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</font></font></mn>
|
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<mo data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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−</font></font>
|
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</mo>
|
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<msup data-moz-translations-id=36>
|
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<mi data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
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A
|
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</font></font></mi>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
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<mn data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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|
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<msup data-moz-translations-id=40>
|
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<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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v
|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
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<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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</font></font></mn>
|
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|
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|
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</mrow>
|
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<mo data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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)
|
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|
|
</font></font></mo>
|
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</mrow>
|
|||
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</mrow>
|
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<mo data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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]
|
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|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
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<mn data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
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|
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</msup>
|
|||
|
|
</mrow>
|
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|
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</mfrac>
|
|||
|
|
</mrow>
|
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|
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</mstyle>
|
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|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {3{\mathfrak {A}}\varrho A}{2s\left[x^{2}+\varrho ^{2}\left(1-A^{2}v^{2 }\right)\right]^{3}}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</font></center>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The magnitude of the movement that occurs dependss primarily on the size</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {3ve^{2}A^{2}(1-A^{2}v^{2})\varrho }{2s\left[x^{2}+\varrho ^{2}\left(1-A^{2}v^{2}\right)\right]^{3}}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
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<mfrac data-moz-translations-id=7>
|
|||
|
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<mrow data-moz-translations-id=8>
|
|||
|
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<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
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<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=11>
|
|||
|
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<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
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<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
|||
|
|
</font></font></mn>
|
|||
|
|
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|
|||
|
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</msup>
|
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|
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<msup data-moz-translations-id=15>
|
|||
|
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<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
|||
|
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|
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|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
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<mn data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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2
|
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|
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|
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|
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|
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|
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</msup>
|
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|
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<mo stretchy=false data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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(
|
|||
|
|
</font></font></mo>
|
|||
|
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<mn data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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1
|
|||
|
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</font></font></mn>
|
|||
|
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<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
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<msup data-moz-translations-id=22>
|
|||
|
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<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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A
|
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|
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</font></font></mi>
|
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|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
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|
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<mn data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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|
|
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|
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|
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</mrow>
|
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</msup>
|
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|
|
<msup data-moz-translations-id=26>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mn data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo stretchy=false data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=32>
|
|||
|
|
<mn data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msup data-moz-translations-id=35>
|
|||
|
|
<mrow data-moz-translations-id=36>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
[
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=38>
|
|||
|
|
<msup data-moz-translations-id=39>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=41>
|
|||
|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msup data-moz-translations-id=44>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
|||
|
|
<mn data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mrow data-moz-translations-id=48>
|
|||
|
|
<mo data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=50>
|
|||
|
|
<mn data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=53>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=55>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<msup data-moz-translations-id=57>
|
|||
|
|
<mi data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=59>
|
|||
|
|
<mn data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
]
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=63>
|
|||
|
|
<mn data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=65><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {3ve^{2}A^{2}(1-A^{2}v^{2})\varrho }{2s\left[x^{2}+\varrho ^{2 }\left(1-A^{2}v^{2}\right)\right]^{3}}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>away. With constant</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>e</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>and and</font> </font><i data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>s</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>it has a maximum for</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle v={\frac {1}{{\sqrt {3}}A}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mn data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow data-moz-translations-id=11>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<msqrt data-moz-translations-id=13>
|
|||
|
|
<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</msqrt>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle v={\frac {1}{{\sqrt {3}}A}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>and is the same</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {e^{2}A}{{\sqrt {3}}s}}.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mrow data-moz-translations-id=8>
|
|||
|
|
<msup data-moz-translations-id=9>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=11>
|
|||
|
|
<mn data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<msqrt data-moz-translations-id=16>
|
|||
|
|
<mn data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
</msqrt>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {e^{2}A}{{\sqrt {3}}s}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>In cathode rays we have electrical charges that fly through space at almost as high a speed.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Let's assume there would be</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 6\cdot 10^{4}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
6
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
⋅</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=8>
|
|||
|
|
<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
10
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
|
<mn data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
4
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 6\cdot 10^{4}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:6.221ex;height:2.676ex alt="{\displaystyle 6\cdot 10^{4}}" data-moz-translations-id=13></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>electrostatic units are transported per second and if we take the speed to be a third of the speed of light, then a tube 50 cm long would constantly have a charge of</font></font><span class=mwe-math-element data-moz-translations-id=14><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=15><math xmlns=http://www.w3.org/1998/Math/
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=18>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=19>
|
|||
|
|
<mn data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
3
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
⋅</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msup data-moz-translations-id=22>
|
|||
|
|
<mn data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
10
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=24>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mn data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
4
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 3\cdot 10^{-4}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:7.499ex;height:2.676ex alt="{\displaystyle 3\cdot 10^{-4}}" data-moz-translation
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=34>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle x=0}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:5.591ex;height:2.176ex alt="{\displaystyle x=0}" data-moz-translations-id=39></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>and and</font></font><span class=mwe-math-element data-moz-translations-id=40><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=41><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varrho =1{\rm {mm}}}" data-moz-translations-id=42><semantics data-moz-translations-id=43>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=44>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=45>
|
|||
|
|
<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ϱ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mn data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
m
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
m
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varrho =1{\rm {mm}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-inver
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {1}{2}}10^{-13}{\frac {1}{s}}.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mfrac data-moz-translations-id=7>
|
|||
|
|
<mn data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<msup data-moz-translations-id=10>
|
|||
|
|
<mn data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
10
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mn data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
13
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<mfrac data-moz-translations-id=16>
|
|||
|
|
<mn data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
s
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {1}{2}}10^{-13}{\frac {1}{s}}.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Outside the tube, noticeable movements would only occur if the ether density was extremely low.</font> </font><span data-moz-translations-id=0><span class=pagenum id=ix title="Page:Translatoric movement of light ether.djvu/9" data-moz-translations-id=1><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[</font> </font><b data-moz-translations-id=3><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/9 title="Page:Translatoric movement of light ether.djvu/9" data-moz-translations-id=4><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>ix</font></font></a></b><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>]</font></font></span></span></span><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>Nothing definite can be said about the events in the immediate vicinity of the cargo.</font> </font><sup id=cite_ref-1 class=reference data-moz-translations-id=5><a href=#cite_note-1 data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[1] [1]</font></font></a></sup></p>
|
|||
|
|
<div style=text-align:center>
|
|||
|
|
<h3><span class=mw-headline id=Reflexion_an_bewegten_durchsichtigen_Medien. data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Reflection on moving transparent media.</font></font></span></h3>
|
|||
|
|
</div>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>An example where the tensions in the aether would cause movement is the reflection of electromagnetic plane waves at the boundary of moving insulators. Let us denote the angle of incidence by</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \varphi }" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \varphi }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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 class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.838ex;width:1.52ex;height:2.176ex alt="{\displaystyle \varphi }" data-moz-translations-id=8></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>, with the index</font> </font><i data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>e</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>the incident components, with</font> </font><i data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>r</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>the reflected components, is according to the known laws</font></font></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle Y_{e}=\sin \left({\frac {x\ \sin \varphi +z_{1}\cos \varphi }{\lambda }}-{\frac {t}{T}}\right)2\pi ,}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<msub data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<mfrac data-moz-translations-id=16>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=19>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msub data-moz-translations-id=24>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mn data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=33>
|
|||
|
|
<mfrac data-moz-translations-id=34>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle Y_{e}=\sin \left({\frac {x\ \sin \varphi +z_{1}\cos \varphi }{\lambda }}-{\frac {t}{T}}\ right)2\pi ,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<msub data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=23>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msub data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=30>
|
|||
|
|
<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mfrac data-moz-translations-id=38>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle L_{e}=\cos \varphi \sin \left({\frac {x\ \sin \varphi +z_{1}\cos \varphi }{\lambda }}-{\frac {t}{ T}}\right)2\pi ,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
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<msub data-moz-translations-id=6>
|
|||
|
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<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
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|
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<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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e
|
|||
|
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</font></font></mi>
|
|||
|
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</mrow>
|
|||
|
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</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
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<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
|
|||
|
|
<mfrac data-moz-translations-id=21>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=24>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<msub data-moz-translations-id=29>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mn data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mfrac data-moz-translations-id=39>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle N_{e}=-\sin \varphi \sin \left({\frac {x\ \sin \varphi +z_{1}\cos \varphi }{\lambda }}-{\frac {t} {T}}\right)2\pi .}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>If we move the plate with the speed</font> </font><i data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>v</font></font></i><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>in the direction</font> </font><i data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>z</font></font></i><font style=vertical-align:inherit> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0> </span> <font style=vertical-align:inherit data-moz-translations-id=2>for the reflected waves</font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit></font></span></p>
|
|||
|
|
<table width=100%>
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td valign=center style=text-align:left width=5%></td>
|
|||
|
|
<td align=center><span class=mwe-math-element><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=0><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle Y_{r}=R\ \sin \left({\frac {x\ \sin \varphi -z_{1}\cos \varphi }{\lambda }}+{\frac {A^{2}vz_{1}}{T}}-{\frac {t}{T}}\right)2\pi ,}" data-moz-translations-id=1><semantics data-moz-translations-id=2>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=3>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=4>
|
|||
|
|
<msub data-moz-translations-id=5>
|
|||
|
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<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
Y
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
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<mi data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=11>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=14>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mfrac data-moz-translations-id=18>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=21>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msub data-moz-translations-id=26>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=28>
|
|||
|
|
<mn data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=35>
|
|||
|
|
<mfrac data-moz-translations-id=36>
|
|||
|
|
<mrow data-moz-translations-id=37>
|
|||
|
|
<msup data-moz-translations-id=38>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=40>
|
|||
|
|
<mn data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msub data-moz-translations-id=43>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mn data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=49>
|
|||
|
|
<mfrac data-moz-translations-id=50>
|
|||
|
|
<mi data-moz-translations-id=51><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle Y_{r}=R\ \sin \left({\frac {x\ \sin \varphi -z_{1}\cos \varphi }{\lambda }}+{\frac {A^{2} vz_{1}}{T}}-{\frac {t}{T}}\right)2\pi ,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<msub data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
L
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=13>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=23>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msub data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=30>
|
|||
|
|
<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mfrac data-moz-translations-id=38>
|
|||
|
|
<mrow data-moz-translations-id=39>
|
|||
|
|
<msup data-moz-translations-id=40>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
|
<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msub data-moz-translations-id=45>
|
|||
|
|
<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
|||
|
|
<mn data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
|
<mfrac data-moz-translations-id=52>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=59><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle L_{r}=-R\ \sin \left({\frac {x\ \sin \varphi -z_{1}\cos \varphi }{\lambda }}+{\frac {A^{2 }vz_{1}}{T}}-{\frac {t}{T}}\right)2\pi ,}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<msub data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
N
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mi data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
r
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=13>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=16>
|
|||
|
|
<mo data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=18>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=23>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<msub data-moz-translations-id=28>
|
|||
|
|
<mi data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=30>
|
|||
|
|
<mn data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mi data-moz-translations-id=32><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=34><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=37>
|
|||
|
|
<mfrac data-moz-translations-id=38>
|
|||
|
|
<mrow data-moz-translations-id=39>
|
|||
|
|
<msup data-moz-translations-id=40>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
A
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=42>
|
|||
|
|
<mn data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msup>
|
|||
|
|
<mi data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<msub data-moz-translations-id=45>
|
|||
|
|
<mi data-moz-translations-id=46><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=47>
|
|||
|
|
<mn data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
|
<mfrac data-moz-translations-id=52>
|
|||
|
|
<mi data-moz-translations-id=53><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle N_{r}=-R\ \sin \left({\frac {x\ \sin \varphi -z_{1}\cos \varphi }{\lambda }}+{\frac {A^{2 }vz_{1}}{T}}-{\frac {t}{T}}\right)2\pi }
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>based on a coordinate system that moves with the plate. If we relate everything to a fixed coordinate system, we have</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle z_{1}=z-vt}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<msub data-moz-translations-id=6>
|
|||
|
|
<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
</mrow>
|
|||
|
|
</msub>
|
|||
|
|
<mo data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle z_{1}=z-vt}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\mathfrak {T}}={\frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z}}={\frac {2\sin 2\varphi }{\lambda }}R\left\{{\frac {1}{\lambda }}\sin \left({\frac {2z\ \cos \varphi }{\lambda }}-{\frac {2vt\ \cos \varphi }{\lambda }}\right)2\pi \right\},}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=7>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=8><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=10>
|
|||
|
|
<mfrac data-moz-translations-id=11>
|
|||
|
|
<mrow data-moz-translations-id=12>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=14>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=17>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=21>
|
|||
|
|
<mfrac data-moz-translations-id=22>
|
|||
|
|
<mrow data-moz-translations-id=23>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=25>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=26>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
P
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=28>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=31><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
|||
|
|
<mfrac data-moz-translations-id=33>
|
|||
|
|
<mrow data-moz-translations-id=34>
|
|||
|
|
<mn data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mn data-moz-translations-id=38><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=39><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=40><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
R
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mrow data-moz-translations-id=42>
|
|||
|
|
<mo data-moz-translations-id=43><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=44>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=45>
|
|||
|
|
<mfrac data-moz-translations-id=46>
|
|||
|
|
<mn data-moz-translations-id=47><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
1
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=48><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
sin
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=50><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow data-moz-translations-id=51>
|
|||
|
|
<mo data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
(
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow data-moz-translations-id=53>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=54>
|
|||
|
|
<mfrac data-moz-translations-id=55>
|
|||
|
|
<mrow data-moz-translations-id=56>
|
|||
|
|
<mn data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=58><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=59>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=60><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=61><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=62><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=63><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=64><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=65>
|
|||
|
|
<mfrac data-moz-translations-id=66>
|
|||
|
|
<mrow data-moz-translations-id=67>
|
|||
|
|
<mn data-moz-translations-id=68><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=69><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mi data-moz-translations-id=70><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mtext data-moz-translations-id=71>
|
|||
|
|
|
|||
|
|
</mtext>
|
|||
|
|
<mi data-moz-translations-id=72><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
cos
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=73><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mi data-moz-translations-id=74><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
φ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mi data-moz-translations-id=75><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
λ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=76><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
)
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mn data-moz-translations-id=77><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
2
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mi data-moz-translations-id=78><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
π</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=79><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
}
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=80><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=81><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\mathfrak {T}}={\frac {\partial {\mathfrak {R}}}{\partial x}}-{\frac {\partial {\mathfrak {P}}}{\partial z }}={\frac {2\sin 2\varphi }{\lambda }}R\left\{{\frac {1}{\lambda }}\sin \left({\frac {2z\ \cos \varphi }{\lambda }}-{\frac {2vt\ \cos \varphi }{\lambda }}\right)2\pi \right\},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,PHN2ZyB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgd2lkdGg9IjY2Ljk2M2V4IiBoZWlnaHQ9IjYuMTc2ZXgiIHN0eWxlPSJ2ZXJ0aWNhbC1hbGlnbjogLTIuNTA1ZXg7IiB2aWV3Qm94PSIwIC0xNTgwLjcgMjg4MzEgMjY1OS4xIiByb2xlPSJpbWciIGZvY3VzYWJsZT0iZmFsc2UiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgYXJpYS1sYWJlbGxlZGJ5PSJNYXRoSmF4LVNWRy0xLVRpdGxlIj4KPHRpdGxlIGlkPSJNYXRoSmF4LVNWRy0xLVRpdGxlIj57XGRpc3BsYXlzdHlsZSB7XG1hdGhmcmFrIHtUfX09e1xmcmFjIHtccGFydGlhbCB7XG1hdGhmcmFrIHtSfX19e1xwYXJ0aWFsIHh9fS17XGZyYWMge1xwYXJ0aWFsIHtcbWF0aGZyYWsge1B9fX17XHBhcnRpYWwgen19PXtcZnJhYyB7MlxzaW4gMlx2YXJwaGkgfXtcbGFtYmRhIH19UlxsZWZ0XHt7XGZyYWMgezF9e1xsYW1iZGEgfX1cc2luIFxsZWZ0KHtcZnJhYyB7MnpcIFxjb3MgXHZhcnBoaSB9e1xsYW1iZGEgfX0te1xmcmFjIHsydnRcIFxjb3MgXHZhcnBoaSB9e1xsYW1iZGEgfX1ccmlnaHQpMlxwaSBccmlnaHRcfSx9PC90aXRsZT4KPGRlZnMgYXJpYS1oaWRkZW49InRydWUiPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSkZSQUstNTQiIGQ9Ik0yODkgNjg2UTMzOCA2ODYgNDM5IDY2OFQ1NjUgNjQ5UTYwNiA2NDkgNjQxIDY3MlE2NTYgNjgzIDY2NCA2OTBUNjc0IDcwMEw2NzUgNzAxUTY3NiA2OTggNjc2IDY5MlY2ODFMNjQxIDYzNlE2MDggNTkxIDYwMiA1ODhRNTc3IDU3NSA1MjggNTc1UTQ5MCA1NzUgNDM4IDU4M0w0MjYgNTg1TDQxNiA1NzhRMzM1IDUyMCAzMzUgNDY1UTMzNSA0MzcgMzkzIDM2NlQ0NTIgMjU5UTQ1MiAyMjYgNDA2IDE3MVEzODcgMTQ2IDM1MSAxMTVMMzQxIDEwNkwzNTggOTdRNDM4IDU4IDQ3NSA1OFE1MjUgNTggNTk4IDEyNEw2MDggMTMzUTYxNyAxMTkgNjE3IDExOFE2MTcgMTE0IDYwNiAxMDNRNTEzIDAgNDQ4IC0yN0w0MzggLTI1UTQwMSAtMTkgMzM3IDE0VDIzNCA0OFExODYgNDggMTIyIC0zTDExMiAtMTFMMTA2IC0zTDEwMSA1TDExMCAxNVExNjAgNjMgMjA5IDEwNUwyMjQgMTE3SDMxMFEzODQgMTYzIDM4NCAyMTBRMzg0IDIzOCAzMjkgMzAzVDI2MyAzOThRMjYyIDQwMCAyNjIgNDA0UTI2MiA0MjcgMjkwIDQ3NlQzNjggNTgwUTM4MyA1OTYgMzgxIDU5NlEzMTUgNjIyIDIyOCA2MjJRMTU5IDYyMiAxMTggNTkzVDc2IDUxNlE3NiA0ODIgOTYgNDYxVDEzOSA0MzFMMTA3IDM5OUw3NSAzNjdRMzQgNDAzIDM0IDQ3MlEzNCA1MjUgNjQgNTcyVDE0OCA2NTJRMjA3IDY4NiAyODkgNjg2WiI+PC9wYXRoPgo8cGF0aCBzdHJva2Utd2lkdGg9IjEiIGlkPSJFMS1NSk1BSU4tM0QiIGQ9Ik01NiAzNDdRNTYgMzYwIDcwIDM2N0g3MDdRNzIyIDM1OSA3MjIgMzQ3UTcyMiAzMzYgNzA4IDMyOEwzOTAgMzI3SDcyUTU2IDMzMiA1NiAzNDdaTTU2IDE1M1E1NiAxNjggNzIgMTczSDcwOFE3MjIgMTYzIDcyMiAxNTNRNzIyIDE0MCA3MDcgMTMzSDcwUTU2IDE0MCA1NiAxNTNaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KTUFJTi0yMjAyIiBkPSJNMjAyIDUwOFExNzkgNTA4IDE2OSA1MjBUMTU4IDU0N1ExNTggNTU3IDE2NCA1NzdUMTg1IDYyNFQyMzAgNjc1VDMwMSA3MTBMMzMzIDcxNUgzNDVRMzc4IDcxNSAzODQgNzE0UTQ0NyA3MDMgNDg5IDY2MVQ1NDkgNTY4VDU2NiA0NTdRNTY2IDM2MiA1MTkgMjQwVDQwMiA1M1EzMjEgLTIyIDIyMyAtMjJRMTIzIC0yMiA3MyA1NlE0MiAxMDIgNDIgMTQ4VjE1OVE0MiAyNzYgMTI5IDM3MFQzMjIgNDY1UTM4MyA0NjUgNDE0IDQzNFQ0NTUgMzY3TDQ1OCAzNzhRNDc4IDQ2MSA0NzggNTE1UTQ3OCA2MDMgNDM3IDYzOVQzNDQgNjc2UTI2NiA2NzYgMjIzIDYxMlEyNjQgNjA2IDI2NCA1NzJRMjY0IDU0NyAyNDYgNTI4VDIwMiA1MDhaTTQzMCAzMDZRNDMwIDM3MiA0MDEgNDAwVDMzMyA0MjhRMjcwIDQyOCAyMjIgMzgyUTE5NyAzNTQgMTgzIDMyM1QxNTAgMjIxUTEzMiAxNDkgMTMyIDExNlExMzIgMjEgMjMyIDIxUTI0NCAyMSAyNTAgMjJRMzI3IDM1IDM3NCAxMTJRMzg5IDEzNyA0MDkgMTk2VDQzMCAzMDZaIj48L3BhdGg+CjxwYXRoIHN0cm9rZS13aWR0aD0iMSIgaWQ9IkUxLU1KRlJBSy01MiIgZD0iTTI3IDQ5NlEzMSA1NjkgMTAyIDYyN1QyMzQgNjg1UTIzNiA2ODUgMjQxIDY4NVQyNTEgNjg2UTI4NyA2ODYgMzE4IDY3MlQzNjcgNjM4VDM5OSA1OThUNDE4IDU2NEw0MjMgNTUwUTQyNCA1NTQgNDM0IDU2N1Q0NjMgNjAxVDUwNSA2MzlUNTYxIDY3MVQ2MjYgNjg1UTY3MiA2ODUgNjg4IDY1OVQ3MTAgNTcyUTcxMyA1MzMgNzIxIDUyM1Q3NjYgNTEzUTc4MSA1MTMgNzg3IDUxNFQ3OTQgNTE2UTc5NiA1MTIgNzk4IDUwOVQ4MDEgNTA0VDgwMiA1MDFUNzg3IDQ5M1E3MDIgNDYxIDYyNCA0MDFMNjA3IDM4OVE2NTUgMzgzIDY4OCAzNThMNjk3IDM1MlYzNDJRNjk5IDMzMCA2OTkgMjk3UTcwNCAyMDkgNzEwIDE3M1Q3MzQgMTAzUTc1MSA2OSA3NjUgNjlRNzY5IDY5IDgwNiA4M0w4MjQgOTBWNzRRODIzIDczIDc1OSAyNFQ2OTMgLTI2UTY5MiAtMjYgNjYwIDMyTDYyOCA5MEw2MjkgMTExUTYzMSAxNTkgNjMxIDE3N1E2MzEgMjc4IDYxNCAzMDBRNTg0IDM0MCA1MjMgMzQwUTUwMCAzNDAgNDY3IDMzM1Q0MzEgMzI1UTQyOSAzMjUgNDI5IDMyMlE0MjggMzIxIDQyNiAzMDhUNDIwIDI3NVQ0MTAgMjMwVDM5MiAxNzhUMzY2IDEyNUwzNTggMTEyTDM0MiA5OVEzMDYgNzAgMjY5IDM4VDIxMyAtMTBUMTkzIC0yNlExOTIgLTI2IDE2MyAwVDExNiAyNlE4MiAyNiA1MCAtOEw0MiAtMTZMMzUgLThMMjcgMEwzNSAxMFE0MyAyMSA1OCAzOFQxMDQgODBUMTU4IDEwNlExNzkgMTA2IDIxOCA2NUwyMzUgNDhRMjM4IDQ4IDI1NSA2MFQyOTUgOTlUMzI5IDE1OFEzNTIgMjMxIDM1MiAzNTlRMzUyIDU1NSAyNDIgNjE0UTIxMCA2MjggMTg3IDYyOFExNDAgNjI4IDExNiA2MDBUOTEgNTQ4UTkxIDUyMiAxMzggNDY0VDE4NSAzODJWMzc2UTE4NSAzNDUgMTU4IDMx
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Let's sit</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 0={\frac {\partial \alpha }{\partial x}}+{\frac {\partial \gamma }{\partial z}},}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=17>
|
|||
|
|
<mfrac data-moz-translations-id=18>
|
|||
|
|
<mrow data-moz-translations-id=19>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial \alpha }{\partial x}}+{\frac {\partial \gamma }{\partial z}},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>so</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle \alpha ={\frac {\partial \psi }{\partial z}}\quad \gamma =-{\frac {\partial \psi }{\partial x}},}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mi data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
α</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mspace width=1em data-moz-translations-id=16></mspace>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=20>
|
|||
|
|
<mfrac data-moz-translations-id=21>
|
|||
|
|
<mrow data-moz-translations-id=22>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=24><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=25>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=27><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=28><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=29><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle \alpha ={\frac {\partial \psi }{\partial z}}\quad \gamma =-{\frac {\partial \psi }{\partial x}},}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>this is how the equations result</font></font></p>
|
|||
|
|
<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 0={\frac {\partial {\mathfrak {T}}}{\partial t}}+{\frac {\partial \psi }{\partial z}}{\frac {\partial {\mathfrak {T}}}{\partial x}}-{\frac {\partial \psi }{\partial x}}{\frac {\partial {\mathfrak {T}}}{\partial z,}}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
|||
|
|
<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
|||
|
|
<mn data-moz-translations-id=6><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
0
|
|||
|
|
</font></font></mn>
|
|||
|
|
<mo data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=8>
|
|||
|
|
<mfrac data-moz-translations-id=9>
|
|||
|
|
<mrow data-moz-translations-id=10>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=12>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=13>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=15>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=17><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
t
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
+
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=19>
|
|||
|
|
<mfrac data-moz-translations-id=20>
|
|||
|
|
<mrow data-moz-translations-id=21>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=24>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=26><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=27>
|
|||
|
|
<mfrac data-moz-translations-id=28>
|
|||
|
|
<mrow data-moz-translations-id=29>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=30><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=31>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=32>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=33><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=34>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=36><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mo data-moz-translations-id=37><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
−</font></font>
|
|||
|
|
</mo>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=38>
|
|||
|
|
<mfrac data-moz-translations-id=39>
|
|||
|
|
<mrow data-moz-translations-id=40>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=41><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=42><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
ψ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=43>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=44><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=45><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
x
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=46>
|
|||
|
|
<mfrac data-moz-translations-id=47>
|
|||
|
|
<mrow data-moz-translations-id=48>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=49><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=50>
|
|||
|
|
<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=51>
|
|||
|
|
<mi mathvariant=fraktur data-moz-translations-id=52><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
T
|
|||
|
|
</font></font></mi>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
</mrow>
|
|||
|
|
<mrow data-moz-translations-id=53>
|
|||
|
|
<mi mathvariant=normal data-moz-translations-id=54><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
∂</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mi data-moz-translations-id=55><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
e.g
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=56><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
,
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mrow>
|
|||
|
|
</mfrac>
|
|||
|
|
</mrow>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=57><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle 0={\frac {\partial {\mathfrak {T}}}{\partial t}}+{\frac {\partial \psi }{\partial z}}{\frac {\partial {\mathfrak {T}}}{\partial x}}-{\frac {\partial \psi }{\partial x}}{\frac {\partial {\mathfrak {T}}}{\partial z,}}}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src=data:image/svg+xml;base64,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
|
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>so</font></font></p>
|
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<center><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle {\frac {\partial \psi }{\partial x}}=-v\quad \gamma =v.}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=4>
|
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<mstyle displaystyle=true scriptlevel=0 data-moz-translations-id=5>
|
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<mrow class=MJX-TeXAtom-ORD data-moz-translations-id=6>
|
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<mfrac data-moz-translations-id=7>
|
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<mrow data-moz-translations-id=8>
|
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<mi mathvariant=normal data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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∂</font></font>
|
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</mi>
|
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<mi data-moz-translations-id=10><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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ψ</font></font>
|
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|
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</mi>
|
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</mrow>
|
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|
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<mrow data-moz-translations-id=11>
|
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|
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<mi mathvariant=normal data-moz-translations-id=12><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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∂</font></font>
|
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|
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</mi>
|
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|
|
<mi data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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x
|
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|
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</font></font></mi>
|
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</mrow>
|
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|
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</mfrac>
|
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|
|
</mrow>
|
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|
|
<mo data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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=
|
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</font></font></mo>
|
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<mo data-moz-translations-id=15><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
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|
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−</font></font>
|
|||
|
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</mo>
|
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|
|
<mi data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
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v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mspace width=1em data-moz-translations-id=17></mspace>
|
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|
|
<mi data-moz-translations-id=18><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
γ</font></font>
|
|||
|
|
</mi>
|
|||
|
|
<mo data-moz-translations-id=19><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
=
|
|||
|
|
</font></font></mo>
|
|||
|
|
<mi data-moz-translations-id=20><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
v
|
|||
|
|
</font></font></mi>
|
|||
|
|
<mo data-moz-translations-id=21><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
.
|
|||
|
|
</font></font></mo>
|
|||
|
|
</mstyle>
|
|||
|
|
</mrow>
|
|||
|
|
<annotation encoding=application/x-tex data-moz-translations-id=22><font style=vertical-align:inherit><font style=vertical-align:inherit>
|
|||
|
|
{\displaystyle {\frac {\partial \psi }{\partial x}}=-v\quad \gamma =v.}
|
|||
|
|
</font></font></annotation>
|
|||
|
|
</semantics>
|
|||
|
|
</math></span><img src="data:image/svg+xml;base64,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
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The tension in the aether would only stop when it moves at the same speed as the moving plate. But this only applies to low speeds. For larger ones, rather complicated values would arise, depending on the period of oscillation.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The fact that the co-motion of the ether only eliminates the tensions in the ether to a first approximation is due to the fact that the movement causes aberration of the ray, which, as is well known, cannot be easily explained by the assumption of moving ether.</font></font></p>
|
|||
|
|
<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>It does not seem entirely hopeless to carry out experiments to see whether the aether is carried along in the direction of movement when reflected from rapidly moving plates.</font></font></p>
|
|||
|
|
<div style=text-align:center>
|
|||
|
|
<h3><span class=mw-headline id=Die_Annahme_ruhenden_Aethers. data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The assumption of dormant aether.</font></font></span></h3>
|
|||
|
|
</div>
|
|||
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>From the foregoing, we cannot entirely deny the possibility that the aether is moving. But the difficulties of carrying out such an assumption should already be sufficiently apparent in the examples outlined. As soon as it is possible to do justice to all the facts observed so far, if one considers the ether to be at rest, this path will initially be recommended for its simplicity. However, we then violate a very general mechanical principle </font></font><span data-moz-translations-id=0><span class=pagenum id=xi title="Page:Translatoric movement of the Lichtäthers.djvu/11" data-moz-translations-id=1><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[ </font></font><b data-moz-translations-id=3><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/11 title="Page:Translatoric movement of the Lichtäthers.djvu/11" data-moz-translations-id=4><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xi</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> from the outset, </font><font style=vertical-align:inherit data-moz-translations-id=1>namely the equality of effect and counteraction, if we do not want to assume that the electromagnetic tensions that want to set the ether in motion are canceled out by a certain rigid structure. And in general, if we deny the ether mobility, it becomes a substrate with highly indeterminate properties that we actually only use to make the finite value of the speed of light more understandable.</font></font><span data-moz-translations-id=0><span class=pagenum id=xi title="Page: Translational movement of the light ether.djvu/11" data-moz-translations-id=1><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=2><b data-moz-translations-id=3><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/11 title="Page: Translational movement of the light ether.djvu/11" data-moz-translations-id=4><font style=vertical-align:inherit><font style=vertical-align:inherit>xi</font></font></a></b></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit> if we do not want to assume that the electromagnetic voltages that want to set the ether in motion are lifted by a certain rigid structure. And in general, when we deny it mobility, the aether becomes a substrate of highly indeterminate properties, which we actually only use to make the finite value of the speed of light more understandable.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>But this path will be particularly recommended to anyone who is initially only interested in the most general presentation of the facts.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The assumption of a resting aether was actually that advocated by </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Fresnel</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> , although there is still talk of a partial continuation of the aether. However, this continuation only takes place inside the weighable bodies as soon as they themselves are moved and can be completely replaced by the view that what is continued is not the ether itself, but the part of the electromagnetic energy that is present in ponderable bodies liable. This emerges very clearly in the calculation by </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Reiff </font></font></span><sup id=cite_ref-2 class=reference data-moz-translations-id=2><a href=#cite_note-2 data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[2]</font></font></a></sup><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> , which shows that the </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=4><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Fresnel</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> coefficient of continuation for a light ray in a moving medium results when the ether itself is at rest, the electromagnetic energy partly in the ether, partly in of the ponderable substance is present.</font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=4></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>continuation of a beam of light in the moving medium, when the aether itself rests, the electromagnetic energy is thematically present in the aether, then in the ponderable substance.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>A precise implementation of the theory based on the assumption of resting ether and unchangeably charged ions as well as a complete discussion of all essential observation results is contained in the work of HA </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lorentz </font></font></span><sup id=cite_ref-3 class=reference data-moz-translations-id=1><a href=#cite_note-3 data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[3]</font></font></a></sup><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> . E. </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Wiechert </font></font></span><sup id=cite_ref-4 class=reference data-moz-translations-id=4><a href=#cite_note-4 data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[4]</font></font></a></sup><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> starts from very similar points of view </font><font style=vertical-align:inherit data-moz-translations-id=1>.</font></font></p>
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<p><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit></font></span><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit>Lorentz </font></font></span><font style=vertical-align:inherit><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit>Fresnel'</font></span></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit></font></span><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit></font></span><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2></span><span data-moz-translations-id=3><span class=pagenum id=xii title="Page:Translatoric movement of Lichtäs.djvu/12" data-moz-translations-id=4><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=5><b data-moz-translations-id=6><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/12 title="Page:Translatoric movement of Lichtäs.djvu/12" data-moz-translations-id=7></a></b></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>introduces where</font></font><span data-moz-translations-id=3><span class=pagenum id=xii title="Page: Translational movement of the light ether.djvu/12" data-moz-translations-id=4><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit>[ </font></font><b data-moz-translations-id=6><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/12 title="Page: Translational movement of the light ether.djvu/12" data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>xii</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit> ]</font></font></span></span></span><font style=vertical-align:inherit></font><i data-moz-translations-id=8></i><span class=mwe-math-element data-moz-translations-id=9><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=10><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle t-t_{1}vA}" data-moz-translations-id=11><semantics data-moz-translations-id=12>
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<annotation encoding=application/x-tex data-moz-translations-id=23><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle t-t_{1}vA}
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</font></font></annotation>
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</semantics>
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</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.671ex;width:
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</font></font><span class=mwe-math-element data-moz-translations-id=25><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=26><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle t_{1}}" data-moz-translations-id=27><semantics data-moz-translations-id=28>
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<annotation encoding=application/x-tex data-moz-translations-id=35><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle t_{1}}
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</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.671ex;width:1.894ex;height:2.343ex alt="{\displaystyle t_{1}}" data-moz-translations-id=36></span><font style=vertical-align:inherit><font style=vertical-align:inherit>the time means that the light uses to get from a fixed point to an arbitrary considered in free Aether, and </font></font><i data-moz-translations-id=37></i><font style=vertical-align:inherit><font style=vertical-align:inherit>is the ratio of the body's speed to the speed of light.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>There is a further correction element for the continuation coefficient, which is caused by the fact that the movement also causes a change in the oscillation period according to the </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Doppler</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> principle. It also immediately follows that the influence of the earth's motion is </font></font><i data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>only</font></font></i><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> shown in the aberration and that the prismatic deflection and the observation of the wavelength are not influenced by gratings. It also follows that a stationary current does not have an inductive effect on another wire due to the movement of the earth, because the movement creates an electrostatic charge which compensates for the effect.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>With the induction effect, the influence of the earth's movement only occurs in proportion to the size</font></font><span class=mwe-math-element data-moz-translations-id=0><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=1><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle v^{2}A^{2}}" data-moz-translations-id=2><semantics data-moz-translations-id=3>
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<mi data-moz-translations-id=7><font style=vertical-align:inherit><font style=vertical-align:inherit>
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v
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</font></font></mi>
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<mn data-moz-translations-id=9><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
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<msup data-moz-translations-id=10>
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<mi data-moz-translations-id=11><font style=vertical-align:inherit><font style=vertical-align:inherit>
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A
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</font></font></mi>
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<mn data-moz-translations-id=13><font style=vertical-align:inherit><font style=vertical-align:inherit>
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2
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<annotation encoding=application/x-tex data-moz-translations-id=14><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle v^{2}A^{2}}
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</font></font></annotation>
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</semantics>
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</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:4.979ex;height:2.676ex alt="{\displaystyle v^{2}A^{2}}" data-moz-translations-id=15></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>so there is no prospect of experimental confirmation.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>After Lorentz</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's theory, which has been worked out in detail, </font><font style=vertical-align:inherit data-moz-translations-id=1>proves that the assumption of immobile ether is completely sufficient to interpret a number of the diverse and hitherto little-explained phenomena of the influence of movement on electromagnetic processes, we must now point out a difficulty of a fundamental nature with consistent implementation of this theory.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>This difficulty is closely related to the fact that changing electromagnetic states give rise to forces that would set the aether in motion if it were mobile. Let us imagine a body in the free ether in the form of a thin plate, which has different radiating capacities for heat rays on both sides. Since, according to </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Maxwell</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's theory, the emitted rays exert a pressure on the surface, this pressure would predominate on the side of the greater radiation and set the body in motion. </font></font><span data-moz-translations-id=1><span class=pagenum id=xiii title="Page:Translatoric movement of light ether.djvu/13" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[ </font></font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/13 title="Page:Translatoric movement of light ether.djvu/13" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xiii</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> So here we have the case that a body sets its center of gravity in motion through its own internal energy. So if we assume the ether to be immobile, then there would be a violation of the general principle of the center of gravity. On the other hand, the assumption of mobile ether, which has inertia, would avoid this objection.</font></font><span data-moz-translations-id=1><span class=pagenum id=xiii title="Page: Translational movement of the light ether.djvu/13" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit>[ </font></font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/13 title="Page: Translational movement of the light ether.djvu/13" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit>xiii</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit> We would therefore have the case that a body sets its center of gravity in motion through its own inner energy. If we therefore accept the ether as immobile, there would be a violation of the general sentence from the center of gravity. On the other hand, the assumption of movable ethers, which possesses inertia, would escape this objection.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>However, the principle of the center of gravity may possibly be of a special nature and be limited to certain groups of effects in which no moving forces occur in the ether, as is actually the case with the usually observed ponderomotive effects.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Under all circumstances, this point should be kept in mind for further theoretical training.</font></font></p>
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<div style=text-align:center>
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<h3><span class=mw-headline id=Die_Versuchsergebnisse. data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The test results.</font></font></span></h3>
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</div>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>After we have discussed the two theoretical setups that are to be separated from each other, let us take a look at the experiments that have been carried out so far.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The main experiments that relate to our question are as follows:</font></font></p>
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<div style=text-align:center>
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<h4><span class=mw-headline id=A._Versuche_mit_positivem_Ergebniss. data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>A. Experiments with positive results.</font></font></span></h4>
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</div>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>1. The aberration of the light of the fixed stars. As is well known, the aberration found a simple explanation through the emission hypothesis of light. The difficulties in the undulation theory have only recently been eliminated by HA </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lorentz</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> by assuming a ether </font></font><i data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>at rest</font></font></i><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> .</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>2. The </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Doppler</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> principle is of general kinematic importance in its nature, but must still be taken into account when considering the question of moving or resting aether.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>3. Fizeau</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiment </font><font style=vertical-align:inherit data-moz-translations-id=1>and its repetition by </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Michelson</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> and </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Morley</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> . A ray of light passing through flowing water in the direction of movement experiences an acceleration of the passage in proportion</font></font><span class=mwe-math-element data-moz-translations-id=3><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=4><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle 1+v(1-(1/n^{2}))}" data-moz-translations-id=5><semantics data-moz-translations-id=6>
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<annotation encoding=application/x-tex data-moz-translations-id=25><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle 1+v(1-(1/n^{2}))}
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</semantics>
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</math></span><img src=data:image/svg+xml;base64,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<div style=text-align:center>
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<h4><span class=mw-headline id=B._Versuche_mit_negativem_Ergebniss. data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>B. Experiments with negative results.</font></font></span></h4>
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</div>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>1. Arago's</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> experiment </font><font style=vertical-align:inherit data-moz-translations-id=1>as to whether the movement of the earth influences the refraction of the light coming from the fixed stars.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>2. </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Ketteler</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ’s interference experiment. The two beams of an interferential refractor are sent through two tubes filled with water and inclined towards each other in such a way that one beam hits one tube after the first reflection (on one glass plate), the other beam hits the second tube after the second reflection (on the other glass plate), i.e. runs in the opposite direction. Although both tubes are carried along by the earth's movement, there is no change in the interference fringes, although one beam is accelerated and the other is delayed.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Both results follow directly from the assumption of resting aether.</font></font></p>
|
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>3. Klinkerfues</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ' experiment </font><font style=vertical-align:inherit data-moz-translations-id=1>to determine whether the absorption line of sodium vapor was influenced by the movement of the earth.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Klinkerfues</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ' positive result </font><font style=vertical-align:inherit data-moz-translations-id=1>would be incompatible with the theory of resting aether. However, the shift found is so small that observation errors cannot be ruled out.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>4. Des Coudres</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiment </font><font style=vertical-align:inherit data-moz-translations-id=1>as to whether the induction effect of two coils of wire on a third is influenced by the fact that the direction of the induction of each coil falls once in the direction of the earth's movement, then in the direction perpendicular to it.</font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit>determine</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit> the induction effect of two wire rollers to a third by the fact that the direction of induction each roll once in the direction of the earth's movement, then falls into the perpendicular one.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>HA </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lorentz</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> has proven that when the aether is at rest, this influence only depends on the square of the ratio of the speed of the earth to the speed of light, and is therefore not observable because the movement of the earth creates an electrostatic charge on the current conductors, which cancels out the first-order effect.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>5. Lodge</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiments </font><font style=vertical-align:inherit data-moz-translations-id=1>to investigate to what extent the surrounding aether is carried along by the movement of heavy or magnetizable masses.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>6. Zehnder</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiments </font><font style=vertical-align:inherit data-moz-translations-id=1>as to whether the ether </font><font style=vertical-align:inherit data-moz-translations-id=2>is moved</font></font><span data-moz-translations-id=1><span class=pagenum id=xv title="Page:Translatoric movement of light ether.djvu/15" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/15 title="Page:Translatoric movement of light ether.djvu/15" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> xv</font></font></a></b></span></span></span><span data-moz-translations-id=1><span class=pagenum id=xv title="Page: Translational movement of the light ether.djvu/15" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/15 title="Page: Translational movement of the light ether.djvu/15" data-moz-translations-id=5></a></b></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>moved by the</font> </font><span data-moz-translations-id=1><span class=pagenum id=xv title="Page: Translational movement of the light ether.djvu/15" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[</font> </font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/15 title="Page: Translational movement of the light ether.djvu/15" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xv</font></font></a></b><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>]</font></font></span></span></span><font style=vertical-align:inherit> <font style=vertical-align:inherit data-moz-translations-id=0>movement of a piston in an air-thinned room.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The experiments of both observers were carried out with sensitive interference methods and gave negative results, so they are in perfect agreement with the assumption of a resting aether.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>7. Mascart</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiments </font><font style=vertical-align:inherit data-moz-translations-id=1>on the rotation of the plane of polarization in quartz. There was no change in rotation when the light rays were once in the direction of the earth's movement and then in the opposite direction.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>HA </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lorentz</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> gave the theory of this phenomenon and found that, assuming the aether is at rest, the earth's movement changes the existing rotation and independently adds a second one.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The negative result of </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Mascart</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's observations would show that in quartz these two rotations caused by the influence of the earth's movement just cancel each other out.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>8. Roentgen</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's experiment to determine </font><font style=vertical-align:inherit data-moz-translations-id=1>whether magnetic forces are generated by the movement of the earth from a charged capacitor.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The negative result of this experiment is not compatible with the assumption of a resting aether.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Electric charges and magnets would also have to produce magnetic or electrical forces through the movement of the earth. The absence of these forces would also be incompatible with the requirement of a resting aether.</font></font></p>
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<p><font style=vertical-align:inherit></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>9. Fizeau</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's </font><font style=vertical-align:inherit data-moz-translations-id=1>experiment on the influence of the earth's movement on the rotation of the plane of polarization through glass columns. </font><font style=vertical-align:inherit data-moz-translations-id=2>The positive result of this experiment has recently been questioned. It would </font><font style=vertical-align:inherit data-moz-translations-id=3>not be compatible with the assumption of resting aether according to HA </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Lorentz</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> 's investigations .</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>10. The </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Michelson</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> and </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Morley</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> experiment . If the aether is at rest, the time it takes for a ray of light to travel back and forth between two plates of glass must change as the plates move. The change depends on the size</font></font><span class=mwe-math-element data-moz-translations-id=2><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style=display:none data-moz-translations-id=3><math xmlns=http://www.w3.org/1998/Math/MathML alttext="{\displaystyle v^{2}A^{2}}" data-moz-translations-id=4><semantics data-moz-translations-id=5>
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<annotation encoding=application/x-tex data-moz-translations-id=16><font style=vertical-align:inherit><font style=vertical-align:inherit>
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{\displaystyle v^{2}A^{2}}
|
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</font></font></annotation>
|
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</semantics>
|
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</math></span><img src="data:image/svg+xml;base64,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" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden=true style=vertical-align:-0.338ex;width:4.979ex;height:2.676ex alt="{\displaystyle v^{2}A^{2}}" data-moz-translations-id=17></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>but should be observable when interference is used.</font></font></p>
|
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<p> <span style=display:none data-moz-translations-id=0></span><span data-moz-translations-id=1><span class=pagenum id=xvi title="Page:Translatoric movement of Lichtäthers.djvu/16" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[ </font></font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/16 title="Page:Translatoric movement of Lichtäthers.djvu/16" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xvi</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> The negative result is incompatible with the assumption of resting aether. This assumption can only be maintained by the hypothesis that the length dimensions of solid bodies are changed in the same proportion by the movement through the resting ether in order to compensate for the lengthening of the path of the light ray.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The assumption of moving aether would give rise to the possibility that the aether is carried along by the movement of the earth and rests relative to it. This would explain all negative test results. But then the explanation of the aberration would remain.</font></font></p>
|
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<div style=text-align:center>
|
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<h3><span id=Gravitation_und_Tr.C3.A4gheit. data-moz-translations-id=0></span><span class=mw-headline id=Gravitation_und_Trägheit. data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Gravity and inertia.</font></font></span></h3>
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</div>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The fact that gravity occupies an exceptional position and has no noticeable relationship to the other natural phenomena has often been emphasized. Its attribution to pressure forces is made more difficult by the fact that the energy reserve of a gravitating system has its greatest value when the individual parts of the mass are at an infinite distance. However, it is not always emphasized clearly enough that the acceleration of heavy masses is most likely related to gravity, because two independent definitions of mass are obtained through acceleration and gravity, which, as far as the very precise observations here go, are perfect to match. If one demands a further explanation of gravity, it would also have to give an account of why work is required to accelerate heavy masses. The fact that the two definitions of mass agree would then have to be a consequence of this explanation. It cannot be said with certainty whether such a theory can also be based on the ether, but it is probable.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>However, it must also be emphasized here that it is by no means certain whether all effects can be traced back to tensions in the ether, just as it remains doubtful whether the processes in the ether can be completely satisfactorily represented by the laws of mechanics.</font></font></p>
|
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<p> <span style=display:none data-moz-translations-id=0></span><span data-moz-translations-id=1><span class=pagenum id=xvii title="Page:Translatoric movement of the light ether.djvu/17" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[ </font></font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/17 title="Page:Translatoric movement of the light ether.djvu/17" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xvii</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> If we now summarize the results, the impression is that there are still a number of questions to be answered before we can decide on the path to be taken by science.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>As we have seen, the assumption of moving ether without inertia leads to improbable consequences.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>As an experiment that would be important for this assumption, we recommend trying to see whether the ether is set in motion by the movement of reflecting transparent media.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>But since the ether is not set in motion by the movement of solid bodies, as far as is known so far, a negative result is likely.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>The following difficulties stand in the way of the assumption that the ether is completely at rest:</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>1. Violation of the principle of the center of gravity (regarding the equality of effect and counteraction).</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>2. The negative results of the experiments of </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Michelson</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> and </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Morley</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> , that of </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Roentgen</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> and possibly the experiments of </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Mascart</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> and </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=4><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Fizeau</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> .</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>It would therefore be urgently desirable to repeat the following experiments or to carry out new ones.</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>1. Does the earth's movement affect the rotation of the plane of polarization</font></font></p>
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<dl>
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<dd><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>
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a) naturally rotating substances,
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</font></font></dd>
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</dl>
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<dl>
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<dd><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>
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b) through glass columns.
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</font></font></dd>
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</dl>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>2. Does the movement of the earth cause the magnetic forces required by the theory through the movement of electrical charges and the corresponding electrical forces through the movement of magnets?</font></font></p>
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<p><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>When the results of these experiments are completely clear, it will become clear whether the otherwise simple theory of resting aether should be retained or abandoned. Should it have to be abandoned, it seems to me that only the </font><font style=vertical-align:inherit data-moz-translations-id=1>way out indicated by </font></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=0><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>Des Coudres</font></font></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> would remain; namely influence of gravity on the light ether. This assumption seems to me to be equivalent to the assumption of a low inertial mass of the light ether.</font></font></p>
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<p> <span style=display:none data-moz-translations-id=0></span><span data-moz-translations-id=1><span class=pagenum id=xviii title="Page:Translatoric movement of light ether.djvu/18" data-moz-translations-id=2><span class="pagenumber noprint" style=color:#666666;display:inline;margin:0px;padding:0px data-moz-translations-id=3><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>[ </font></font><b data-moz-translations-id=4><a href=https://de.wikisource.org/wiki/Seite%3ATranslatorische_Bewegung_des_Licht%C3%A4thers.djvu/18 title="Page:Translatoric movement of light ether.djvu/18" data-moz-translations-id=5><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0>xviii</font></font></a></b><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> ]</font></font></span></span></span><font style=vertical-align:inherit><font style=vertical-align:inherit data-moz-translations-id=0> It would then be explained that the earth pulls the ether with it due to its significant gravity, while the movement of small solid bodies on the earth has no influence. The negative result of the experiments mentioned would be easily explained.</font></font></p>
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<p><font style=vertical-align:inherit data-moz-translations-id=0></font><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>But then the difficulties in explaining the aberration to which HA Lorentz</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5>drew attention</font> <font style=vertical-align:inherit data-moz-translations-id=6>would essentially remain .</font> <font style=vertical-align:inherit data-moz-translations-id=7>However, whether these cannot be overcome if the co-movement of the ether under the influence of gravity is taken into account requires a special investigation. For this purpose, the hydrodynamic problem would have to be solved to determine the movements of a liquid through which a point moves with a constant speed, which attracts the individual parts of the according to the according to the movements of a liquid through which a point moves with a constant speed, which attracts the individual parts of the according to</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9><font style=vertical-align:inherit data-moz-translations-id=10>Newton</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12>'s law.</font></font></p>
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>The The</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3><font style=vertical-align:inherit data-moz-translations-id=4>Maxwell</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>'s tensions that would set the ether in motion are always so small, because the appear appear multiplied by the reciprocal speed of light, that the movements generally become imperceptible even with a very small inertial mass.</font></font></p>
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<p><font style=vertical-align:inherit data-moz-translations-id=0><font style=vertical-align:inherit data-moz-translations-id=1>The task of theory would then be to look for examples where the movement of the ether could actually be observed.</font></font></p>
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<li id=cite_note-1><span class=mw-cite-backlink data-moz-translations-id=0><a href=#cite_ref-1 aria-label="Jump high" title=Jump-jumping data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>↑</font></font></a></span> <span class=reference-text data-moz-translations-id=4><font style=vertical-align:inherit data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6>I used</font></font> <span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=7><font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>Jamin</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11>'s interferential refractor to test whether a light beam passing through a vacuum tube is accelerated by the cathode rays; but the result was definite negative.</font></font></span></li>
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<li id=cite_note-2><span class=mw-cite-backlink data-moz-translations-id=0><a href=#cite_ref-2 aria-label="Jump high" title=Jump-jumping data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>↑ </font></font></a></span> <span class=reference-text data-moz-translations-id=4><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>Reiff</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>, Wied. Ann. 50. p. 367. 1893</font></font></span></li>
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<li id=cite_note-3><span class=mw-cite-backlink data-moz-translations-id=0><a href=#cite_ref-3 aria-label="Jump high" title=Jump-jumping data-moz-translations-id=1><font style=vertical-align:inherit data-moz-translations-id=2><font style=vertical-align:inherit data-moz-translations-id=3>↑ </font></font></a></span> <span class=reference-text data-moz-translations-id=4><span style=letter-spacing:0.2em;left:0.1em data-moz-translations-id=5><font style=vertical-align:inherit data-moz-translations-id=6><font style=vertical-align:inherit data-moz-translations-id=7>Lorentz</font></font></span> <font style=vertical-align:inherit data-moz-translations-id=8><font style=vertical-align:inherit data-moz-translations-id=9>,</font></font> <a href="https://de-wikisource-org.translate.goog/wiki/Versuch_einer_Theorie_der_electrischen_und_optischen_Erscheinungen_in_bewegten_K%C3%B6rpern?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-US" title="Attempt of a theory of electric and optical phenomena in moving bodies" data-moz-translations-id=10><font style=vertical-align:inherit data-moz-translations-id=11><font style=vertical-align:inherit data-moz-translations-id=12>attempt at a theory of electrical and optical phenomena in moving bodies</font></font></a> <font style=vertical-align:inherit data-moz-translations-id=13><font style=vertical-align:inherit data-moz-translations-id=14>. Leyden 1895 [WS:Template:1893].</font></font></span></li>
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