CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="eu" dir="ltr"> <head> <meta charset="UTF-8"> <title>Lagrangeren mekanika - Wikipedia, entziklopedia askea.</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )euwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t.",".\t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","urtarrila","otsaila","martxoa","apirila","maiatza","ekaina","uztaila","abuztua","iraila","urria","azaroa","abendua"],"wgRequestId":"73f03fe0-0966-4030-aeb0-fd4a33ca1a96","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Lagrangeren_mekanika","wgTitle":"Lagrangeren mekanika","wgCurRevisionId":7865977,"wgRevisionId":7865977,"wgArticleId":60481,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Wikipedia:GND identifikatzailea duten artikuluak","Fisika zirriborroak","Lagrangeren mekanika"],"wgPageViewLanguage":"eu","wgPageContentLanguage":"eu","wgPageContentModel":"wikitext","wgRelevantPageName":"Lagrangeren_mekanika","wgRelevantArticleId":60481,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false, "wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"eu","pageLanguageDir":"ltr","pageVariantFallbacks":"eu"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":1000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q324669","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready", "ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.categoryTree.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.categoryTree","site","mediawiki.page.ready","jquery.makeCollapsible","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ErrefAurrebista","ext.gadget.UkensKonkurranse","ext.gadget.TxikipediaTab","ext.gadget.ArtikuluenKalitatea","ext.gadget.refToolbar","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging", "ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=eu&modules=ext.categoryTree.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=eu&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=eu&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Lagrangeren mekanika - Wikipedia, entziklopedia askea."> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//eu.m.wikipedia.org/wiki/Lagrangeren_mekanika"> <link rel="alternate" type="application/x-wiki" title="Aldatu" href="/w/index.php?title=Lagrangeren_mekanika&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (eu)"> <link rel="EditURI" type="application/rsd+xml" href="//eu.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://eu.wikipedia.org/wiki/Lagrangeren_mekanika"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eu"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom Jarioa" href="/w/index.php?title=Berezi:AzkenAldaketak&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Lagrangeren_mekanika rootpage-Lagrangeren_mekanika skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Edukira joan</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Menu nagusia" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Menu nagusia</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Menu nagusia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ezkutatu</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Nabigazioa </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Azala" title="Azala bisitatu [z]" accesskey="z"><span>Azala</span></a></li><li id="n-Txikipedia" class="mw-list-item"><a href="/wiki/Txikipedia:Azala"><span>Txikipedia</span></a></li><li id="n-Ikusgela" class="mw-list-item"><a href="/wiki/Atari:Hezkuntza/Ikusgela"><span>Ikusgela</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Txokoa" title="Proiektuaren inguruan, zer egin dezakezu, non aurkitu nahi duzuna"><span>Txokoa</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Berezi:AzkenAldaketak" title="Wikiko azken aldaketen zerrenda. [r]" accesskey="r"><span>Aldaketa berriak</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Berezi:Ausazkoa" title="Ausazko orrialde bat kargatu [x]" accesskey="x"><span>Ausazko orria</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Laguntza:Sarrera" title="Aurkitzeko lekua."><span>Laguntza</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Azala" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Entziklopedia askea" src="/static/images/mobile/copyright/wikipedia-tagline-eu.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </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="/wiki/Berezi:Bilatu" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia(e)n bilatu [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Bilatu</span> </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="Wikipedia wikian bilatu" aria-label="Wikipedia wikian bilatu" autocapitalize="sentences" title="Wikipedia(e)n bilatu [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Berezi:Bilatu"> </div> <button class="cdx-button cdx-search-input__end-button">Bilatu</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Tresna pertsonalak"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itxura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itxura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </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-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu" class=""><span>Dohaintza egin</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:KontuaSortu&returnto=Lagrangeren+mekanika" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea." class=""><span>Sortu kontua</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:SaioaHasi&returnto=Lagrangeren+mekanika" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o" class=""><span>Hasi saioa</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="Aukera gehiago" > <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="Tresna pertsonalak" > <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">Tresna pertsonalak</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu"><span>Dohaintza egin</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:KontuaSortu&returnto=Lagrangeren+mekanika" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Sortu kontua</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:SaioaHasi&returnto=Lagrangeren+mekanika" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Edukiak" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Eduki taularen ikusgarritasuna aldatu" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-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-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Eduki taularen ikusgarritasuna aldatu</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Lagrangeren mekanika</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Joan beste hizkuntza batean idatzitako artikulu batera. 40 hizkuntzatan eskuragarri." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-40" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">40 hizkuntza</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Lagrange-meganika" title="Lagrange-meganika – afrikaansa" lang="af" hreflang="af" data-title="Lagrange-meganika" data-language-autonym="Afrikaans" data-language-local-name="afrikaansa" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D9%84%D8%A7%D8%BA%D8%B1%D8%A7%D9%86%D8%AC" title="ميكانيكا لاغرانج – arabiera" lang="ar" hreflang="ar" data-title="ميكانيكا لاغرانج" data-language-autonym="العربية" data-language-local-name="arabiera" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%B0%D0%B2%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Лагранжава механіка – bielorrusiera" lang="be" hreflang="be" data-title="Лагранжава механіка" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0_%D0%BD%D0%B0_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6" title="Механика на Лагранж – bulgariera" lang="bg" hreflang="bg" data-title="Механика на Лагранж" data-language-autonym="Български" data-language-local-name="bulgariera" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Formulaci%C3%B3_lagrangiana" title="Formulació lagrangiana – katalana" lang="ca" hreflang="ca" data-title="Formulació lagrangiana" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%BB%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Лагранжла механика – txuvaxera" lang="cv" hreflang="cv" data-title="Лагранжла механика" data-language-autonym="Чӑвашла" data-language-local-name="txuvaxera" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Lagrange-Formalismus" title="Lagrange-Formalismus – alemana" lang="de" hreflang="de" data-title="Lagrange-Formalismus" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%B1%CE%B3%CE%BA%CF%81%CE%B1%CE%BD%CE%B6%CE%B9%CE%B1%CE%BD%CE%AE_%CE%BC%CE%B7%CF%87%CE%B1%CE%BD%CE%B9%CE%BA%CE%AE" title="Λαγκρανζιανή μηχανική – greziera" lang="el" hreflang="el" data-title="Λαγκρανζιανή μηχανική" data-language-autonym="Ελληνικά" data-language-local-name="greziera" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Lagrangian_mechanics" title="Lagrangian mechanics – ingelesa" lang="en" hreflang="en" data-title="Lagrangian mechanics" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Lagran%C4%9Da_mekaniko" title="Lagranĝa mekaniko – esperantoa" lang="eo" hreflang="eo" data-title="Lagranĝa mekaniko" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Mec%C3%A1nica_lagrangiana" title="Mecánica lagrangiana – gaztelania" lang="es" hreflang="es" data-title="Mecánica lagrangiana" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Lagrange%27i_mehaanika" title="Lagrange'i mehaanika – estoniera" lang="et" hreflang="et" data-title="Lagrange'i mehaanika" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9_%D9%84%D8%A7%DA%AF%D8%B1%D8%A7%D9%86%DA%98%DB%8C" title="مکانیک لاگرانژی – persiera" lang="fa" hreflang="fa" data-title="مکانیک لاگرانژی" data-language-autonym="فارسی" data-language-local-name="persiera" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Lagrangen_mekaniikka" title="Lagrangen mekaniikka – finlandiera" lang="fi" hreflang="fi" data-title="Lagrangen mekaniikka" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89quations_de_Lagrange" title="Équations de Lagrange – frantsesa" lang="fr" hreflang="fr" data-title="Équations de Lagrange" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Mec%C3%A1nica_lagranxiana" title="Mecánica lagranxiana – galiziera" lang="gl" hreflang="gl" data-title="Mecánica lagranxiana" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%94_%D7%9C%D7%92%D7%A8%D7%90%D7%A0%D7%96%27%D7%99%D7%AA" title="מכניקה לגראנז'ית – hebreera" lang="he" hreflang="he" data-title="מכניקה לגראנז'ית" data-language-autonym="עברית" data-language-local-name="hebreera" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BE%E0%A4%97%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%9C%E0%A5%80%E0%A4%AF_%E0%A4%AF%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80" title="लाग्रांजीय यांत्रिकी – hindia" lang="hi" hreflang="hi" data-title="लाग्रांजीय यांत्रिकी" data-language-autonym="हिन्दी" data-language-local-name="hindia" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mekanika_Lagrangian" title="Mekanika Lagrangian – indonesiera" lang="id" hreflang="id" data-title="Mekanika Lagrangian" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Meccanica_lagrangiana" title="Meccanica lagrangiana – italiera" lang="it" hreflang="it" data-title="Meccanica lagrangiana" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5%E5%8A%9B%E5%AD%A6" title="ラグランジュ力学 – japoniera" lang="ja" hreflang="ja" data-title="ラグランジュ力学" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Mekanika_Lagrangian" title="Mekanika Lagrangian – javera" lang="jv" hreflang="jv" data-title="Mekanika Lagrangian" data-language-autonym="Jawa" data-language-local-name="javera" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F%D1%81%D1%8B" title="Лагранж функциясы – kazakhera" lang="kk" hreflang="kk" data-title="Лагранж функциясы" data-language-autonym="Қазақша" data-language-local-name="kazakhera" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9D%BC%EA%B7%B8%EB%9E%91%EC%A3%BC_%EC%97%AD%ED%95%99" title="라그랑주 역학 – koreera" lang="ko" hreflang="ko" data-title="라그랑주 역학" data-language-autonym="한국어" data-language-local-name="koreera" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B4%97%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B4%9E%E0%B5%8D%E0%B4%9A%E0%B4%BF%E0%B4%AF%E0%B5%BB_%E0%B4%AC%E0%B4%B2%E0%B4%A4%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82" title="ലഗ്രാഞ്ചിയൻ ബലതന്ത്രം – malabarera" lang="ml" hreflang="ml" data-title="ലഗ്രാഞ്ചിയൻ ബലതന്ത്രം" data-language-autonym="മലയാളം" data-language-local-name="malabarera" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lagrangiaanse_mechanica" title="Lagrangiaanse mechanica – nederlandera" lang="nl" hreflang="nl" data-title="Lagrangiaanse mechanica" data-language-autonym="Nederlands" data-language-local-name="nederlandera" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Lagrangemekanikk" title="Lagrangemekanikk – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Lagrangemekanikk" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Lagrange-mekanikk" title="Lagrange-mekanikk – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Lagrange-mekanikk" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Mechanika_Lagrange%E2%80%99a" title="Mechanika Lagrange’a – poloniera" lang="pl" hreflang="pl" data-title="Mechanika Lagrange’a" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Mec%C3%A2nica_de_Lagrange" title="Mecânica de Lagrange – portugesa" lang="pt" hreflang="pt" data-title="Mecânica de Lagrange" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Mecanic%C4%83_lagrangian%C4%83" title="Mecanică lagrangiană – errumaniera" lang="ro" hreflang="ro" data-title="Mecanică lagrangiană" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%B5%D0%B2%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Лагранжева механика – errusiera" lang="ru" hreflang="ru" data-title="Лагранжева механика" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Lagrangeeva_formulacija_gibalnih_ena%C4%8Db" title="Lagrangeeva formulacija gibalnih enačb – esloveniera" lang="sl" hreflang="sl" data-title="Lagrangeeva formulacija gibalnih enačb" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Mekanika_e_Lagranzhit" title="Mekanika e Lagranzhit – albaniera" lang="sq" hreflang="sq" data-title="Mekanika e Lagranzhit" data-language-autonym="Shqip" data-language-local-name="albaniera" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Lagranges_ekvationer" title="Lagranges ekvationer – suediera" lang="sv" hreflang="sv" data-title="Lagranges ekvationer" data-language-autonym="Svenska" data-language-local-name="suediera" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%A5%E0%B8%B2%E0%B8%81%E0%B8%A3%E0%B9%87%E0%B8%AD%E0%B8%87%E0%B8%8C%E0%B9%8C" title="กลศาสตร์ลากร็องฌ์ – thailandiera" lang="th" hreflang="th" data-title="กลศาสตร์ลากร็องฌ์" data-language-autonym="ไทย" data-language-local-name="thailandiera" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Lagrange_mekani%C4%9Fi" title="Lagrange mekaniği – turkiera" lang="tr" hreflang="tr" data-title="Lagrange mekaniği" data-language-autonym="Türkçe" data-language-local-name="turkiera" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0_%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%B0" title="Механіка Лагранжа – ukrainera" lang="uk" hreflang="uk" data-title="Механіка Лагранжа" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%C6%A1_h%E1%BB%8Dc_Lagrange" title="Cơ học Lagrange – vietnamera" lang="vi" hreflang="vi" data-title="Cơ học Lagrange" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E5%8A%9B%E5%AD%A6" title="拉格朗日力学 – txinera" lang="zh" hreflang="zh" data-title="拉格朗日力学" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q324669#sitelinks-wikipedia" title="Aldatu hizkuntzen arteko loturak" class="wbc-editpage">Aldatu loturak</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Izen-tarteak"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Lagrangeren_mekanika" title="Eduki orrialdea ikusi [c]" accesskey="c"><span>Artikulua</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Eztabaida:Lagrangeren_mekanika&action=edit&redlink=1" rel="discussion" class="new" title="Artikuluari buruzko eztabaida (sortu gabe) [t]" accesskey="t"><span>Eztabaida</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Aldatu hizkuntza aldaera" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">euskara</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Ikusketak"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Lagrangeren_mekanika"><span>Irakurri</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&veaction=edit" title="Orri hau aldatu [v]" accesskey="v"><span>Aldatu</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&action=edit" title="Idatzi orri honen iturburu kodea [e]" accesskey="e"><span>Aldatu iturburu kodea</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&action=history" title="Artikulu honen aurreko bertsioak. [h]" accesskey="h"><span>Ikusi historia</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tresnak" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tresnak</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tresnak</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ezkutatu</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Ekintzak </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Lagrangeren_mekanika"><span>Irakurri</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&veaction=edit" title="Orri hau aldatu [v]" accesskey="v"><span>Aldatu</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&action=edit" title="Idatzi orri honen iturburu kodea [e]" accesskey="e"><span>Aldatu iturburu kodea</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&action=history"><span>Ikusi historia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Orokorra </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Berezi:ZerkLotzenDuHona/Lagrangeren_mekanika" title="Orri honetaranzko esteka duten wiki orri guztien zerrenda [j]" accesskey="j"><span>Honanzko esteka duten orriak</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Berezi:RecentChangesLinked/Lagrangeren_mekanika" rel="nofollow" title="Orri honetatik esteka duten orrietako azken aldaketak [k]" accesskey="k"><span>Lotutako orrietako aldaketak</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=eu" title="Irudiak edo media fitxategiak igo [u]" accesskey="u"><span>Fitxategia igo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Berezi:OrrialdeBereziak" title="Orri berezi guztien zerrenda [q]" accesskey="q"><span>Orri bereziak</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&oldid=7865977" title="Orriaren bertsio honetaranzko esteka iraunkorra"><span>Lotura iraunkorra</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&action=info" title="Orrialde honi buruzko informazio gehiago"><span>Orri honen datuak</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Berezi:CiteThisPage&page=Lagrangeren_mekanika&id=7865977&wpFormIdentifier=titleform" title="Orri honen aipua egiteko moduari buruzko informazioa"><span>Artikulu hau aipatu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Berezi:UrlShortener&url=https%3A%2F%2Feu.wikipedia.org%2Fwiki%2FLagrangeren_mekanika"><span>URL laburra lortu</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Berezi:QrCode&url=https%3A%2F%2Feu.wikipedia.org%2Fwiki%2FLagrangeren_mekanika"><span>QR kodea jaitsi</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Inprimatu/esportatu </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Berezi:Book&bookcmd=book_creator&referer=Lagrangeren+mekanika"><span>Liburu bat sortu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Berezi:DownloadAsPdf&page=Lagrangeren_mekanika&action=show-download-screen"><span>Deskargatu PDF formatuan</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Lagrangeren_mekanika&printable=yes" title="Orrialde honen bertsio inprimagarria [p]" accesskey="p"><span>Inprimatzeko bertsioa</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Beste proiektuetan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q324669" title="Datuen biltegi elementu batera lotuta [g]" accesskey="g"><span>Wikidata itema</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Itxura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ezkutatu</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Wikipedia, Entziklopedia askea</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r9236167">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><style data-mw-deduplicate="TemplateStyles:r9235570">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><style data-mw-deduplicate="TemplateStyles:r9249993">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:#f8f9fa;border:1px solid #aaa;padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Artikulu sorta honen partea:</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="/wiki/Mekanika_klasiko" title="Mekanika klasiko">Mekanika klasikoa</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0e889207254cfbfab613b8beba214f5e4d2430d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.49ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}"></span><div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></div></td></tr><tr><th class="sidebar-heading" style="background:#ddf; display:block;margin-bottom:1.0em;"> <div class="hlist"> <ul><li><a href="/wiki/Mekanika_klasikoaren_historia" title="Mekanika klasikoaren historia">Historia</a></li> <li><a href="/wiki/Mekanika_Klasikoaren_kronologia" class="mw-redirect" title="Mekanika Klasikoaren kronologia">Kronologia</a></li></ul> </div></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Adarrak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Mekanika_aplikatua" title="Mekanika aplikatua">Aplikatua</a></li> <li><a href="/wiki/Dinamika" title="Dinamika">Dinamika</a></li> <li><a href="/wiki/Estatika" title="Estatika">Estatika</a></li> <li><a href="/wiki/Zeruko_mekanika" title="Zeruko mekanika">Zerukoa</a></li> <li><a href="/wiki/Zinematika" title="Zinematika">Zinematika</a></li> <li><a href="/wiki/Medio_jarraituen_mekanika" title="Medio jarraituen mekanika">Medio jarraituak</a></li> <li><a href="/w/index.php?title=Zinetika_(fisika)&action=edit&redlink=1" class="new" title="Zinetika (fisika) (sortu gabe)">Zinetika</a></li> <li><a href="/w/index.php?title=Fisika_estatistiko&action=edit&redlink=1" class="new" title="Fisika estatistiko (sortu gabe)">Estatistikoa</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Oinarriak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Abiadura" title="Abiadura">Abiadura</a></li> <li><a href="/wiki/Azelerazio" title="Azelerazio">Azelerazioa</a></li> <li><a href="/wiki/Abiadura-modulu" class="mw-redirect" title="Abiadura-modulu">Abiadura-modulua</a></li> <li><a href="/wiki/Bulkada_(fisika)" title="Bulkada (fisika)">Bulkada</a></li> <li><a href="/w/index.php?title=D%27Alembert-en_printzipioa&action=edit&redlink=1" class="new" title="D'Alembert-en printzipioa (sortu gabe)">D'Alembert-en printzipioa</a></li> <li><a href="/wiki/Denbora" title="Denbora">Denbora</a></li> <li><a href="/wiki/Energia" title="Energia">Energia</a> <ul><li><a href="/wiki/Energia_potentzial" title="Energia potentzial">potentziala</a></li> <li><a href="/wiki/Energia_zinetiko" title="Energia zinetiko">zinetikoa</a></li></ul></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Erreferentzia-sistema_inertzial" title="Erreferentzia-sistema inertzial">Erreferentzia-sistema inertziala</a></li> <li><a href="/wiki/Erreferentzia-sistema_ez-inertzial" title="Erreferentzia-sistema ez-inertzial">Erreferentzia-sistema ez-inertziala</a></li> <li><a href="/wiki/Espazio" title="Espazio">Espazioa</a></li> <li><a href="/wiki/Indar-pare" title="Indar-pare">Indar-parea</a></li> <li><a href="/wiki/Indar" title="Indar">Indarra</a></li> <li><span style="white-space:nowrap"><a href="/wiki/Inertzia" title="Inertzia">Inertzia</a> / <a href="/wiki/Inertzia-momentu" title="Inertzia-momentu">Inertzia-momentua</a></span></li> <li><a href="/wiki/Lan_(fisika)" title="Lan (fisika)">Lana</a></li> <li><a href="/w/index.php?title=Lan_birtual&action=edit&redlink=1" class="new" title="Lan birtual (sortu gabe)">Lan birtuala</a></li> <li><a href="/wiki/Masa" title="Masa">Masa</a></li> <li><a href="/w/index.php?title=Momentu_(fisika)&action=edit&redlink=1" class="new" title="Momentu (fisika) (sortu gabe)">Momentua</a></li> <li><a href="/wiki/Momentu_angeluar" title="Momentu angeluar">Momentu angeluarra</a></li> <li><a href="/wiki/Momentu_lineal" title="Momentu lineal">Momentu lineala</a></li> <li><a href="/wiki/Potentzia" title="Potentzia">Potentzia</a></li> <li><a href="/wiki/Torke" class="mw-redirect" title="Torke">Torkea</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Zientzialariak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/w/index.php?title=Jeremiah_Horrocks&action=edit&redlink=1" class="new" title="Jeremiah Horrocks (sortu gabe)">Horrocks</a></li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Halley</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Clairaut</a></li> <li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Lagrange</a></li> <li><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Muinekoak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Bibrazio" title="Bibrazio">Bibrazioa</a></li> <li><a href="/wiki/Desplazamendu_(fisika)" title="Desplazamendu (fisika)">Desplazamendua</a></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Erreferentzia-sistema_inertzial" title="Erreferentzia-sistema inertzial">Erreferentzia-sistema inertziala</a></li> <li><a href="/wiki/Erreferentzia-sistema_ez-inertzial" title="Erreferentzia-sistema ez-inertzial">Erreferentzia-sistema ez-inertziala</a></li> <li><a href="/wiki/Gorputz_zurrun" title="Gorputz zurrun">Gorputz zurruna</a> <ul><li><a href="/w/index.php?title=Eulerren_ekuazio&action=edit&redlink=1" class="new" title="Eulerren ekuazio (sortu gabe)">Eulerren ekuazioa</a></li> <li><a href="/w/index.php?title=Solido_zurrunaren_mekanika&action=edit&redlink=1" class="new" title="Solido zurrunaren mekanika (sortu gabe)">Solido zurrunaren mekanika</a></li></ul></li> <li><a href="/wiki/Grabitazio_unibertsalaren_legea" title="Grabitazio unibertsalaren legea"><span style="white-space: normal;">Grabitazio unibertsalaren legea</span></a></li> <li><a href="/wiki/Higidura_zuzen" title="Higidura zuzen">Higidura zuzena</a></li> <li><a href="/wiki/Higidura" title="Higidura">Higidura</a></li> <li><a href="/wiki/Marruskadura-indar" title="Marruskadura-indar">Marruskadura-indarra</a></li> <li><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></li> <li><a href="/wiki/Osziladore_harmoniko" title="Osziladore harmoniko">Osziladore harmonikoa</a></li> <li><a href="/w/index.php?title=Moteltze&action=edit&redlink=1" class="new" title="Moteltze (sortu gabe)">Moteltze</a>(<a href="/w/index.php?title=Moteltze_ratio&action=edit&redlink=1" class="new" title="Moteltze ratio (sortu gabe)">Moteltze ratio</a>)</li> <li><a href="/w/index.php?title=Higiduraren_ekuazio&action=edit&redlink=1" class="new" title="Higiduraren ekuazio (sortu gabe)">Higiduraren ekuazioa</a></li> <li><a href="/w/index.php?title=Eulerren_higiduraren_legeak&action=edit&redlink=1" class="new" title="Eulerren higiduraren legeak (sortu gabe)"><span style="white-space: normal;">Eulerren higiduraren legeak</span></a></li> <li><a href="/w/index.php?title=Itxurazko_indar&action=edit&redlink=1" class="new" title="Itxurazko indar (sortu gabe)">Itxurazko indarra</a></li> <li><a href="/w/index.php?title=Partikula_planarraren_higadura-mekanika&action=edit&redlink=1" class="new" title="Partikula planarraren higadura-mekanika (sortu gabe)">Partikula planarraren higadura-mekanika</a></li> <li><a href="/w/index.php?title=Abiadura_erlatibo&action=edit&redlink=1" class="new" title="Abiadura erlatibo (sortu gabe)">Abiadura erlatiboa</a></li> <li><a href="/wiki/Higidura_harmoniko_sinple" title="Higidura harmoniko sinple">Higidura harmoniko sinple</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;"><a href="/wiki/Biraketa-ardatz" title="Biraketa-ardatz">Biraketa</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Abiadura_angeluar" title="Abiadura angeluar">Abiadura angeluarra</a></li> <li><a href="/wiki/Abiadura" title="Abiadura">Abiadura tangentziala</a></li> <li><a href="/w/index.php?title=Azelerazio_angeluar&action=edit&redlink=1" class="new" title="Azelerazio angeluar (sortu gabe)">Azelerazio angeluarra</a></li> <li><a href="/w/index.php?title=Biraketa-abiadura&action=edit&redlink=1" class="new" title="Biraketa-abiadura (sortu gabe)">Biraketa-abiadura</a></li> <li><a href="/wiki/Coriolis_efektua" title="Coriolis efektua">Coriolis efektua</a></li> <li><a href="/w/index.php?title=Desplazamendu_angeluar&action=edit&redlink=1" class="new" title="Desplazamendu angeluar (sortu gabe)">Desplazamendua</a></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Higidura_zirkular" title="Higidura zirkular">Higidura zirkular</a></li> <li><a href="/wiki/Indar_zentripetu" title="Indar zentripetu">Indar zentripetu</a></li> <li><a href="/wiki/Indar_zentrifugo" title="Indar zentrifugo">Indar zentrifugo</a></li> <li><a href="/w/index.php?title=Maiztasun_angeluar&action=edit&redlink=1" class="new" title="Maiztasun angeluar (sortu gabe)">Maiztasuna</a></li> <li><a href="/wiki/Pendulu_(matematika)" class="mw-redirect" title="Pendulu (matematika)">Pendulua</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Formulazioak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></li> <li><a href="/wiki/Mekanika_analitiko" title="Mekanika analitiko">Mekanika analitikoa</a></li> <li><a class="mw-selflink selflink">Mekanika Lagrangiar</a></li> <li><a href="/w/index.php?title=Mekanika_Hamiltoniar&action=edit&redlink=1" class="new" title="Mekanika Hamiltoniar (sortu gabe)">Mekanika Hamiltoniar</a></li> <li><a href="/w/index.php?title=Mekanika_Routhiar&action=edit&redlink=1" class="new" title="Mekanika Routhiar (sortu gabe)">Mekanika Routhiar</a></li> <li><a href="/w/index.php?title=Hamilton%E2%80%93Jacobi_ekuazioa&action=edit&redlink=1" class="new" title="Hamilton–Jacobi ekuazioa (sortu gabe)">Hamilton–Jacobi ekuazioa</a></li> <li><a href="/w/index.php?title=Appellen_higidura-ekuazioa&action=edit&redlink=1" class="new" title="Appellen higidura-ekuazioa (sortu gabe)">Appellen higidura-ekuazioa</a></li> <li><a href="/w/index.php?title=Koopman%E2%80%93von_Neumann_mekanika_klasiko&action=edit&redlink=1" class="new" title="Koopman–von Neumann mekanika klasiko (sortu gabe)">Koopman–von Neumann mekanika</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Kategoriak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"><div class="CategoryTreeTag" data-ct-options="{"mode":0,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Mekanika_klasikoa" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="/wiki/Kategoria:Mekanika_klasikoa" title="Kategoria:Mekanika klasikoa">Mekanika klasikoa</a></bdi></div><div class="CategoryTreeChildren" style="display:none"></div></div></div> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="padding-top:0.15em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9236167"><style data-mw-deduplicate="TemplateStyles:r9235565">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-ikusi"><a href="/wiki/Txantiloi:Mekanika_klasikoa" title="Txantiloi:Mekanika klasikoa"><abbr title="Txantiloi hau ikusi">i</abbr></a></li><li class="nv-eztabaida"><a href="/w/index.php?title=Txantiloi_eztabaida:Mekanika_klasikoa&action=edit&redlink=1" class="new" title="Txantiloi eztabaida:Mekanika klasikoa (sortu gabe)"><abbr title="Txantiloi hau eztabaidatu">e</abbr></a></li><li class="nv-aldatu"><a class="external text" href="https://eu.wikipedia.org/w/index.php?title=Txantiloi:Mekanika_klasikoa&action=edit"><abbr title="Txantiloi hau aldatu">a</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Lagrangeren mekanika</b> <a href="/wiki/Mekanika_klasiko" title="Mekanika klasiko">mekanika klasikoaren</a> formulazioa da, zeinak <a href="/wiki/Momentu_lineal" title="Momentu lineal">momentu lineal</a> eta <a href="/wiki/Energia" title="Energia">energiaren</a> kontserbazioak konbinatzen dituen. <a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph Louis Lagrangek</a> plazaratu zuen <a href="/wiki/1788" title="1788">1788</a>. urtean, hortik bere izena. Lagrangeren mekanikan, partikula-sistema baten ibilbidea <a href="/w/index.php?title=Lagrangeren_ekuazioa&action=edit&redlink=1" class="new" title="Lagrangeren ekuazioa (sortu gabe)">Lagrangeren ekuazioa</a> askatuz lor daiteke, azken hau, sistemaren <a href="/w/index.php?title=Koordenatu_orokortu&action=edit&redlink=1" class="new" title="Koordenatu orokortu (sortu gabe)">koordenatu orokortu</a> bakoitzeko ematen delarik. </p><p>Koordenatu orokor hauen erabilpenak sistema baten analisia asko sinplifika dezake. Formulazio honen beste abantaila batzuen artean, <a href="/wiki/Erreferentzia-sistema_inertzial" title="Erreferentzia-sistema inertzial">erreferentzia-sistema inertzial</a> guztiak berdin tratatzen dituela eta <a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeen</a> ez bezala, higidura ekuazioen forma ez dela erreferentzia sistema inertzialaren menpekoa aurki daitezke. Gainera, erreferentzia-sistema ez-inertziala izatekotan, inertzia indarrak ez dira zertan gehitu behar, baizik eta ondorioztatuak dira. </p> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lagrangeren_mekanika&veaction=edit&section=1" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Lagrangeren_mekanika&action=edit&section=1" title="Edit section's source code: Kanpo estekak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="clear:both;"></div><style data-mw-deduplicate="TemplateStyles:r7786466">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control,.mw-parser-output .mw-mf-linked-projects{border:1px solid #a2a9b1;font-size:88%}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}</style><div class="mw-authority-control"><div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9236167"><style data-mw-deduplicate="TemplateStyles:r9236165">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style></div><div role="navigation" class="navbox" aria-labelledby="Autoritate_kontrola" style="width: inherit;padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritate_kontrola" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Laguntza:Autoritate_kontrola" title="Laguntza:Autoritate kontrola">Autoritate kontrola</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>Wikimedia proiektuak</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q324669" class="extiw" title="wikidata:Q324669">Q324669</a></span></li> <li><b>Identifikadoreak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Integrated_Authority_File" class="mw-redirect" title="Integrated Authority File">GND</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4316154-6">4316154-6</a></span></li> <li><b>Hiztegiak eta entziklopediak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/Lagrange-planetary-equations">url</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q324669" class="extiw" title="wikidata:Q324669">Q324669</a></span></li></ul> </div></div> <p><br /> </p> <table style="width: 100%; padding: 3px; background: #ffffff; border: 1px solid gray; margin: 10px auto; clear: both;" align="center"> <tbody><tr> <td style="float: left; margin: 0 10px;"><span typeof="mw:File"><a href="/wiki/Fitxategi:P_physics.png" class="mw-file-description" title="Fisika"><img alt="Fisika" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/P_physics.png/30px-P_physics.png" decoding="async" width="30" height="26" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/P_physics.png/45px-P_physics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/P_physics.png/60px-P_physics.png 2x" data-file-width="77" data-file-height="68" /></a></span> </td> <td>Artikulu hau <a href="/wiki/Fisika" title="Fisika">fisikari</a> buruzko <b><a href="/wiki/Wikipedia:Zirriborro" title="Wikipedia:Zirriborro">zirriborroa</a></b> da. Wikipedia lagun dezakezu edukia <a class="external text" href="https://eu.wikipedia.org/w/index.php?title=Lagrangeren_mekanika&action=edit">osatuz</a>. </td></tr></tbody></table>    </div><script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("Gadget \"ErrefAurrebista\" was not loaded. Please migrate it to use ResourceLoader. See \u003Chttps://eu.wikipedia.org/wiki/Berezi:Gadgetak\u003E.");});</script><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://eu.wikipedia.org/w/index.php?title=Lagrangeren_mekanika&oldid=7865977">https://eu.wikipedia.org/w/index.php?title=Lagrangeren_mekanika&oldid=7865977</a>"(e)tik eskuratuta</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Berezi:Kategoriak" title="Berezi:Kategoriak">Kategoriak</a>: <ul><li><a href="/wiki/Kategoria:Fisika_zirriborroak" title="Kategoria:Fisika zirriborroak">Fisika zirriborroak</a></li><li><a href="/wiki/Kategoria:Lagrangeren_mekanika" title="Kategoria:Lagrangeren mekanika">Lagrangeren mekanika</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Ezkutuko kategoria: <ul><li><a href="/wiki/Kategoria:Wikipedia:GND_identifikatzailea_duten_artikuluak" title="Kategoria:Wikipedia:GND identifikatzailea duten artikuluak">Wikipedia:GND identifikatzailea duten artikuluak</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Orriaren azken aldaketa: 4 maiatza 2020, 19:46.</li> <li id="footer-info-copyright">Testua <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eu">Creative Commons Aitortu-PartekatuBerdin 4.0 lizentziari</a> jarraituz erabil daiteke; baliteke beste klausularen batzuk ere aplikatu behar izatea. Xehetasunen berri izateko, ikus <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">erabilera-baldintzak</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Pribazitate politika</a></li> <li id="footer-places-about"><a href="/wiki/Laguntza:Wikipediari_buruz">Wikipediari buruz</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Erantzukizunen_mugaketa_orokorra">Lege oharra</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Garatzaileak</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/eu.wikipedia.org">Estatistikak</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie adierazpena</a></li> <li id="footer-places-mobileview"><a href="//eu.m.wikipedia.org/w/index.php?title=Lagrangeren_mekanika&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mugikorreko bista</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5c59558b9d-4xt49","wgBackendResponseTime":105,"wgPageParseReport":{"limitreport":{"cputime":"0.184","walltime":"0.321","ppvisitednodes":{"value":336,"limit":1000000},"postexpandincludesize":{"value":30141,"limit":2097152},"templateargumentsize":{"value":6039,"limit":2097152},"expansiondepth":{"value":10,"limit":100},"expensivefunctioncount":{"value":2,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":12497,"limit":5000000},"entityaccesscount":{"value":3,"limit":400},"timingprofile":["100.00% 241.434 1 -total"," 51.56% 124.487 1 Txantiloi:Autoritate_kontrola"," 45.96% 110.974 1 Txantiloi:Mekanika_klasikoa"," 44.26% 106.855 1 Txantiloi:Sidebar_with_collapsible_lists"," 6.16% 14.865 8 Txantiloi:Flatlist"," 2.38% 5.748 1 Txantiloi:Fisika_zirriborroa"," 1.97% 4.764 1 Txantiloi:Nowrap"," 1.42% 3.427 2 Txantiloi:Allow_wrap"," 0.93% 2.251 1 Txantiloi:\\"," 0.84% 2.033 1 Txantiloi:Zirriborro_oinarria"]},"scribunto":{"limitreport-timeusage":{"value":"0.129","limit":"10.000"},"limitreport-memusage":{"value":2511418,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-78f4c97c5d-g84nx","timestamp":"20241129034435","ttl":21600,"transientcontent":true}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Lagrangeren mekanika","url":"https:\/\/eu.wikipedia.org\/wiki\/Lagrangeren_mekanika","sameAs":"http:\/\/www.wikidata.org\/entity\/Q324669","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q324669","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-12-20T16:40:57Z","dateModified":"2020-05-04T18:46:43Z"}</script> </body> </html>