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class="vector-toc-link" href="#Desplazamientos_de_puntos_materiales_aislados"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Desplazamientos de puntos materiales aislados</span> </div> </a> <ul id="toc-Desplazamientos_de_puntos_materiales_aislados-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Desplazamientos_en_un_sólido_deformable" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Desplazamientos_en_un_sólido_deformable"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Desplazamientos en un sólido deformable</span> </div> </a> <ul id="toc-Desplazamientos_en_un_sólido_deformable-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografía" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografía"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografía</span> </div> </a> <ul id="toc-Bibliografía-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="Contenidos" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Desplazamiento (vector)</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="Ir a un artículo en otro idioma. Disponible en 57 idiomas" > <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-57" 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">57 idiomas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%9D%E1%8B%95%E1%88%AB%E1%8D%8D" title="ምዕራፍ (amárico)" lang="am" hreflang="am" data-title="ምዕራፍ" data-language-autonym="አማርኛ" data-language-local-name="amárico" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%B2%D8%A7%D8%AD%D8%A9_(%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1)" title="إزاحة (فيزياء) (árabe)" lang="ar" hreflang="ar" data-title="إزاحة (فيزياء)" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A7%B0%E0%A6%A3" title="সৰণ (asamés)" lang="as" hreflang="as" data-title="সৰণ" data-language-autonym="অসমীয়া" data-language-local-name="asamés" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B0%D0%BC%D1%8F%D1%88%D1%87%D1%8D%D0%BD%D0%BD%D0%B5" title="Перамяшчэнне (bielorruso)" lang="be" hreflang="be" data-title="Перамяшчэнне" data-language-autonym="Беларуская" data-language-local-name="bielorruso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B0%D0%BC%D1%8F%D1%88%D1%87%D1%8D%D0%BD%D1%8C%D0%BD%D0%B5" title="Перамяшчэньне (Belarusian (Taraškievica orthography))" lang="be-tarask" hreflang="be-tarask" data-title="Перамяшчэньне" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%BC%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80)" title="Преместване (вектор) (búlgaro)" lang="bg" hreflang="bg" data-title="Преместване (вектор)" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%B0%E0%A6%A3" title="সরণ (bengalí)" lang="bn" hreflang="bn" data-title="সরণ" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Despla%C3%A7ament_(cinem%C3%A0tica)" title="Desplaçament (cinemàtica) (catalán)" lang="ca" hreflang="ca" data-title="Desplaçament (cinemàtica)" data-language-autonym="Català" data-language-local-name="catalán" 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%9A%D1%83%D2%AB%D0%BD%C4%83%D0%BB%C4%83%D1%85" title="Куҫнăлăх (chuvasio)" lang="cv" hreflang="cv" data-title="Куҫнăлăх" data-language-autonym="Чӑвашла" data-language-local-name="chuvasio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Dadleoliad" title="Dadleoliad (galés)" lang="cy" hreflang="cy" data-title="Dadleoliad" data-language-autonym="Cymraeg" data-language-local-name="galés" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B5%CF%84%CE%B1%CF%84%CF%8C%CF%80%CE%B9%CF%83%CE%B7" title="Μετατόπιση (griego)" lang="el" hreflang="el" data-title="Μετατόπιση" data-language-autonym="Ελληνικά" data-language-local-name="griego" 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/Displacement_(geometry)" title="Displacement (geometry) (inglés)" lang="en" hreflang="en" data-title="Displacement (geometry)" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Siire_(mehaanika)" title="Siire (mehaanika) (estonio)" lang="et" hreflang="et" data-title="Siire (mehaanika)" data-language-autonym="Eesti" data-language-local-name="estonio" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Desplazamendu_(fisika)" title="Desplazamendu (fisika) (euskera)" lang="eu" hreflang="eu" data-title="Desplazamendu (fisika)" data-language-autonym="Euskara" data-language-local-name="euskera" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_%D8%AC%D8%A7%D8%A8%D9%87%E2%80%8C%D8%AC%D8%A7%DB%8C%DB%8C" title="بردار جابه‌جایی (persa)" lang="fa" hreflang="fa" data-title="بردار جابه‌جایی" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9placement_(g%C3%A9om%C3%A9trie)" title="Déplacement (géométrie) (francés)" lang="fr" hreflang="fr" data-title="Déplacement (géométrie)" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A2%D7%AA%D7%A7_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="העתק (פיזיקה) (hebreo)" lang="he" hreflang="he" data-title="העתק (פיזיקה)" data-language-autonym="עברית" data-language-local-name="hebreo" 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%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%AA%E0%A4%A8_(%E0%A4%B8%E0%A4%A6%E0%A4%BF%E0%A4%B6)" title="विस्थापन (सदिश) (hindi)" lang="hi" hreflang="hi" data-title="विस्थापन (सदिश)" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Deplasman" title="Deplasman (criollo haitiano)" lang="ht" hreflang="ht" data-title="Deplasman" data-language-autonym="Kreyòl ayisyen" data-language-local-name="criollo haitiano" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A5%D5%B2%D5%A1%D6%83%D5%B8%D5%AD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6_(%D6%86%D5%AB%D5%A6%D5%AB%D5%AF%D5%A1)" title="Տեղափոխություն (ֆիզիկա) (armenio)" lang="hy" hreflang="hy" data-title="Տեղափոխություն (ֆիզիկա)" data-language-autonym="Հայերեն" data-language-local-name="armenio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Perpindahan" title="Perpindahan (indonesio)" lang="id" hreflang="id" data-title="Perpindahan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" 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/Spostamento_(cinematica)" title="Spostamento (cinematica) (italiano)" lang="it" hreflang="it" data-title="Spostamento (cinematica)" data-language-autonym="Italiano" data-language-local-name="italiano" 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/%E5%A4%89%E4%BD%8D" title="変位 (japonés)" lang="ja" hreflang="ja" data-title="変位" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%83%D1%8B%D1%81%D1%82%D1%8B%D1%80%D1%83" title="Ауыстыру (kazajo)" lang="kk" hreflang="kk" data-title="Ауыстыру" data-language-autonym="Қазақша" data-language-local-name="kazajo" 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%B3%80%EC%9C%84" title="변위 (coreano)" lang="ko" hreflang="ko" data-title="변위" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Poslinkis" title="Poslinkis (lituano)" lang="lt" hreflang="lt" data-title="Poslinkis" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/P%C4%81rvietojums" title="Pārvietojums (letón)" lang="lv" hreflang="lv" data-title="Pārvietojums" data-language-autonym="Latviešu" data-language-local-name="letón" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BC%D0%B5%D1%81%D1%82%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_(%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80)" title="Поместување (вектор) (macedonio)" lang="mk" hreflang="mk" data-title="Поместување (вектор)" data-language-autonym="Македонски" data-language-local-name="macedonio" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BE%E0%B4%A8%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%B0%E0%B4%82" title="സ്ഥാനാന്തരം (malayálam)" lang="ml" hreflang="ml" data-title="സ്ഥാനാന്തരം" data-language-autonym="മലയാളം" data-language-local-name="malayálam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%AA%E0%A4%A8_(%E0%A4%B8%E0%A4%A6%E0%A4%BF%E0%A4%B6)" title="विस्थापन (सदिश) (maratí)" lang="mr" hreflang="mr" data-title="विस्थापन (सदिश)" data-language-autonym="मराठी" data-language-local-name="maratí" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sesaran" title="Sesaran (malayo)" lang="ms" hreflang="ms" data-title="Sesaran" data-language-autonym="Bahasa Melayu" data-language-local-name="malayo" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9B%E1%80%BD%E1%80%B1%E1%80%B7" title="အရွေ့ (birmano)" lang="my" hreflang="my" data-title="အရွေ့" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmano" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Qaxxaamura" title="Qaxxaamura (oromo)" lang="om" hreflang="om" data-title="Qaxxaamura" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A8%BF%E0%A9%B1%E0%A8%A5" title="ਵਿੱਥ (punyabí)" lang="pa" hreflang="pa" data-title="ਵਿੱਥ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punyabí" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przemieszczenie_(fizyka)" title="Przemieszczenie (fizyka) (polaco)" lang="pl" hreflang="pl" data-title="Przemieszczenie (fizyka)" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%D8%AA%DA%BE%D9%91" title="وتھّ (Western Punjabi)" lang="pnb" hreflang="pnb" data-title="وتھّ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Deslocamento" title="Deslocamento (portugués)" lang="pt" hreflang="pt" data-title="Deslocamento" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D1%89%D0%B5%D0%BD%D0%B8%D0%B5" title="Перемещение (ruso)" lang="ru" hreflang="ru" data-title="Перемещение" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Pomeraj" title="Pomeraj (serbocroata)" lang="sh" hreflang="sh" data-title="Pomeraj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Displacement_vector" title="Displacement vector (Simple English)" lang="en-simple" hreflang="en-simple" data-title="Displacement vector" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nhambwe_yasudurukwa" title="Nhambwe yasudurukwa (shona)" lang="sn" hreflang="sn" data-title="Nhambwe yasudurukwa" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Zhvendosja_(fizik%C3%AB)" title="Zhvendosja (fizikë) (albanés)" lang="sq" hreflang="sq" data-title="Zhvendosja (fizikë)" data-language-autonym="Shqip" data-language-local-name="albanés" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D0%BF%D0%BE%D0%BC%D0%B5%D1%80%D0%B0%D1%98%D0%B0" title="Вектор помераја (serbio)" lang="sr" hreflang="sr" data-title="Вектор помераја" data-language-autonym="Српски / srpski" data-language-local-name="serbio" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%9F%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%86%E0%AE%AF%E0%AE%B0%E0%AF%8D%E0%AE%9A%E0%AF%8D%E0%AE%9A%E0%AE%BF" title="இடப்பெயர்ச்சி (tamil)" lang="ta" hreflang="ta" data-title="இடப்பெயர்ச்சி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B1%8D%E0%B0%A5%E0%B0%BE%E0%B0%A8%E0%B0%AD%E0%B1%8D%E0%B0%B0%E0%B0%82%E0%B0%B6%E0%B0%AE%E0%B1%81" title="స్థానభ్రంశము (telugu)" lang="te" hreflang="te" data-title="స్థానభ్రంశము" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%88%E0%B8%B1%E0%B8%94_(%E0%B9%80%E0%B8%A7%E0%B8%81%E0%B9%80%E0%B8%95%E0%B8%AD%E0%B8%A3%E0%B9%8C)" title="การกระจัด (เวกเตอร์) (tailandés)" lang="th" hreflang="th" data-title="การกระจัด (เวกเตอร์)" data-language-autonym="ไทย" data-language-local-name="tailandés" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/%C3%9Dol_we_orun_%C3%BC%C3%BDtgetme" title="Ýol we orun üýtgetme (turcomano)" lang="tk" hreflang="tk" data-title="Ýol we orun üýtgetme" data-language-autonym="Türkmençe" data-language-local-name="turcomano" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Displasmento_(Heometriya)" title="Displasmento (Heometriya) (tagalo)" lang="tl" hreflang="tl" data-title="Displasmento (Heometriya)" data-language-autonym="Tagalog" data-language-local-name="tagalo" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Yer_de%C4%9Fi%C5%9Ftirme_(fizik)" title="Yer değiştirme (fizik) (turco)" lang="tr" hreflang="tr" data-title="Yer değiştirme (fizik)" data-language-autonym="Türkçe" data-language-local-name="turco" 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%9F%D0%B5%D1%80%D0%B5%D0%BC%D1%96%D1%89%D0%B5%D0%BD%D0%BD%D1%8F" title="Переміщення (ucraniano)" lang="uk" hreflang="uk" data-title="Переміщення" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DB%81%D9%B9%D8%A7%D8%A4" title="ہٹاؤ (urdu)" lang="ur" hreflang="ur" data-title="ہٹاؤ" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ko%27chish_(Fizika)" title="Ko'chish (Fizika) (uzbeko)" lang="uz" hreflang="uz" data-title="Ko'chish (Fizika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeko" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Li_%C4%91%E1%BB%99" title="Li độ (vietnamita)" lang="vi" hreflang="vi" data-title="Li độ" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-displacement_vector" title="I-displacement vector (xhosa)" lang="xh" hreflang="xh" data-title="I-displacement vector" data-language-autonym="IsiXhosa" data-language-local-name="xhosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BD%8D%E7%A7%BB" title="位移 (chino)" lang="zh" hreflang="zh" data-title="位移" data-language-autonym="中文" data-language-local-name="chino" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BD%8D%E7%A7%BB" title="位移 (Literary Chinese)" lang="lzh" hreflang="lzh" data-title="位移" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BD%8D%E7%A7%BB" title="位移 (cantonés)" lang="yue" hreflang="yue" data-title="位移" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</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/Q190291#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</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="Espacios de nombres"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet 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mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&action=history" title="Versiones anteriores de esta página [h]" accesskey="h"><span>Ver historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Página de herramientas"> <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="Herramientas" > <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">Herramientas</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">Herramientas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Más opciones" > <div class="vector-menu-heading"> Acciones </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/Desplazamiento_(vector)"><span>Leer</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit" title="Editar esta página [e]" accesskey="e"><span>Editar</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&action=history"><span>Ver historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:LoQueEnlazaAqu%C3%AD/Desplazamiento_(vector)" title="Lista de todas las páginas de la wiki que enlazan aquí [j]" accesskey="j"><span>Lo que enlaza aquí</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:CambiosEnEnlazadas/Desplazamiento_(vector)" rel="nofollow" title="Cambios recientes en las páginas que enlazan con esta [k]" accesskey="k"><span>Cambios en enlazadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=es" title="Subir archivos [u]" accesskey="u"><span>Subir archivo</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginasEspeciales" title="Lista de todas las páginas especiales [q]" accesskey="q"><span>Páginas especiales</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&oldid=158147800" title="Enlace permanente a esta versión de la página"><span>Enlace permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&action=info" title="Más información sobre esta página"><span>Información de la página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Desplazamiento_%28vector%29&id=158147800&wpFormIdentifier=titleform" title="Información sobre cómo citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:Acortador_de_URL&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FDesplazamiento_%28vector%29"><span>Obtener URL acortado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fes.wikipedia.org%2Fwiki%2FDesplazamiento_%28vector%29"><span>Descargar código QR</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"> Imprimir/exportar </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=Especial:Libro&bookcmd=book_creator&referer=Desplazamiento+%28vector%29"><span>Crear un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Desplazamiento_%28vector%29&action=show-download-screen"><span>Descargar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Desplazamiento_(vector)&printable=yes" title="Versión imprimible de esta página [p]" accesskey="p"><span>Versión para imprimir</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"> En otros proyectos </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Displacement_vector" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q190291" title="Enlace al elemento conectado del repositorio de datos [g]" accesskey="g"><span>Elemento de Wikidata</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="Página de herramientas"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Apariencia"> <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">Apariencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</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">De Wikipedia, la enciclopedia libre</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="es" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Archivo:Deslocamento.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Deslocamento.png/235px-Deslocamento.png" decoding="async" width="235" height="126" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Deslocamento.png/353px-Deslocamento.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Deslocamento.png/470px-Deslocamento.png 2x" data-file-width="700" data-file-height="374" /></a><figcaption>La esfera se movió del punto A al punto B</figcaption></figure> <p>En <a href="/wiki/Mec%C3%A1nica" title="Mecánica">mecánica</a>, el <b>desplazamiento</b> es el <a href="/wiki/Vector" title="Vector">vector</a> que define la posición de un punto o <a href="/wiki/Part%C3%ADcula" class="mw-disambig" title="Partícula">partícula</a> en relación con un origen A con respecto a una posición B. El vector se extiende desde el punto de referencia hasta la posición final. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Introducción"><span id="Introducci.C3.B3n"></span>Introducción</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit&section=1" title="Editar sección: Introducción"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En la <a href="/wiki/Din%C3%A1mica_del_punto_material" title="Dinámica del punto material">dinámica del punto material</a>, se entiende por desplazamiento el vector o segmento recto orientado que une la posición inicial con otro punto genérico de la <a href="/wiki/Trayectoria" title="Trayectoria">trayectoria</a>. Este uso del vector desplazamiento permite describir en forma completa el movimiento y el camino de una partícula. </p><p>En <a href="/wiki/Mec%C3%A1nica_de_medios_continuos" title="Mecánica de medios continuos">mecánica de medios continuos</a> se entiende por desplazamiento el vector que va desde la posición inicial (antes de la deformación) a la final (después de la deformación) de un mismo punto material del medio continuo. </p><p>Cuando el punto de referencia es el origen del sistema de coordenadas que se utiliza, el <b>vector desplazamiento</b> se denomina por lo general <a href="/wiki/Vector" title="Vector">vector</a> <a href="/wiki/Posici%C3%B3n" title="Posición">posición</a>, que indica la posición por medio de la línea recta dirigida desde la posición previa a la posición actual, en comparación con la <a href="/wiki/Escalar_(f%C3%ADsica)" title="Escalar (física)">magnitud escalar</a> "distancia recorrida" que indica solo la longitud del camino, obviamente en un espacio euclídeo se tiene: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><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 \|\Delta \mathbf {r} (t)\|\leq L_{r}=\int _{0}^{t}v(t)\ dt=\int _{0}^{t}\left\|{\frac {d\mathbf {r} (t)}{dt}}\right\|\ dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">‖</mo> <mo>≤</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow> <mo symmetric="true">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo symmetric="true">‖</mo> </mrow> <mtext> </mtext> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|\Delta \mathbf {r} (t)\|\leq L_{r}=\int _{0}^{t}v(t)\ dt=\int _{0}^{t}\left\|{\frac {d\mathbf {r} (t)}{dt}}\right\|\ dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc49d24cf2c188bab2a8c76d4e846b7185776de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:44.782ex; height:6.509ex;" alt="{\displaystyle \|\Delta \mathbf {r} (t)\|\leq L_{r}=\int _{0}^{t}v(t)\ dt=\int _{0}^{t}\left\|{\frac {d\mathbf {r} (t)}{dt}}\right\|\ dt}"></span> </p> </blockquote> <p>La igualdad anterior solo se cumpliría para un movimiento rectilíneo. </p><p>Cuando el punto de referencia es la posición previa de la partícula, el <b>vector desplazamiento</b> indica la dirección del movimiento por medio de un vector que va desde la posición previa a la posición actual. Este uso del vector desplazamiento es útil para definir a los vectores velocidad y aceleración de una partícula definida. </p> <div class="mw-heading mw-heading2"><h2 id="Desplazamientos_de_puntos_materiales_aislados">Desplazamientos de puntos materiales aislados</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit&section=2" title="Editar sección: Desplazamientos de puntos materiales aislados"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En ciertos contextos se representa por <b>Δ<sub>x</sub></b> y viene dado por: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><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 \Delta _{x}(t)=x_{t}-x_{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{x}(t)=x_{t}-x_{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16a0ec29ceb83fd9454fc78a0e3d8b953c47e88f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.623ex; height:2.843ex;" alt="{\displaystyle \Delta _{x}(t)=x_{t}-x_{0}\,}"></span> </p> </blockquote> <div class="mw-heading mw-heading2"><h2 id="Desplazamientos_en_un_sólido_deformable"><span id="Desplazamientos_en_un_s.C3.B3lido_deformable"></span>Desplazamientos en un sólido deformable</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit&section=3" title="Editar sección: Desplazamientos en un sólido deformable"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si llamamos K a la región del espacio ocupada por un <a href="/wiki/Mec%C3%A1nica_de_s%C3%B3lidos_deformables" title="Mecánica de sólidos deformables">sólido deformable</a> podemos representar el proceso de deformación entre dos posiciones como un <a href="/wiki/Difeomorfismo" title="Difeomorfismo">difeomorfismo</a> <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 T_{D}:K\to \mathbb {R} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>:</mo> <mi>K</mi> <mo stretchy="false">→</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{D}:K\to \mathbb {R} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f7efbe2197b9239b3abd658f5650a8b7a18ce6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.3ex; height:3.009ex;" alt="{\displaystyle T_{D}:K\to \mathbb {R} ^{3}}"></span>. Si consideramos un <a href="/wiki/Sistema_de_coordenadas" title="Sistema de coordenadas">sistema de coordenadas</a> cartesianas (<i>x, y, z</i>) sobre <i>K</i> se define el vector desplazamiento <i><b>u</b></i> para cada punto sencillamente como: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><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 \mathbf {u} =(u_{x},u_{y},u_{z})=T_{D}(x,y,z)-(x,y,z)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {u} =(u_{x},u_{y},u_{z})=T_{D}(x,y,z)-(x,y,z)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94060139b2dc8722547168309492f394232abf28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:39.851ex; height:3.009ex;" alt="{\displaystyle \mathbf {u} =(u_{x},u_{y},u_{z})=T_{D}(x,y,z)-(x,y,z)\,}"></span> </p> </blockquote> <p>A partir de este vector de desplazamientos es trivial calcular las componentes de la <a href="/wiki/Deformaci%C3%B3n" title="Deformación">deformación</a> y si se conoce la <a href="/wiki/Ecuaci%C3%B3n_constitutiva" title="Ecuación constitutiva">ley constitutiva</a> del sólido deformable pueden determinarse las <a href="/wiki/Tensi%C3%B3n_mec%C3%A1nica" title="Tensión mecánica">tensiones mecánicas</a> a las que se haya sometido. En concreto el <a href="/wiki/Tensor_deformaci%C3%B3n" title="Tensor deformación">tensor deformación</a> de Green-Lagrange: </p> <blockquote style="padding: 5px 10px; background-color: var(--background-color-base, #fff); color: var(--color-base, #202122); text-align: left; margin-left:30px; margin-bottom: 0.4em; margin-top:0.2em; min-width:50%;"> <p><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 \mathbf {D} =(\varepsilon _{ij}),\quad {\mbox{donde}}\ \varepsilon _{ij}={1 \over 2}\left({\partial u_{i} \over \partial x_{j}}+{\partial u_{j} \over \partial x_{i}}+\sum _{k}{\partial u_{k} \over \partial x_{i}}{\partial u_{k} \over \partial x_{j}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>donde</mtext> </mstyle> </mrow> <mtext> </mtext> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {D} =(\varepsilon _{ij}),\quad {\mbox{donde}}\ \varepsilon _{ij}={1 \over 2}\left({\partial u_{i} \over \partial x_{j}}+{\partial u_{j} \over \partial x_{i}}+\sum _{k}{\partial u_{k} \over \partial x_{i}}{\partial u_{k} \over \partial x_{j}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36781151d99040c6e00af1a03834fa1a2ffb376f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:58.609ex; height:7.509ex;" alt="{\displaystyle \mathbf {D} =(\varepsilon _{ij}),\quad {\mbox{donde}}\ \varepsilon _{ij}={1 \over 2}\left({\partial u_{i} \over \partial x_{j}}+{\partial u_{j} \over \partial x_{i}}+\sum _{k}{\partial u_{k} \over \partial x_{i}}{\partial u_{k} \over \partial x_{j}}\right)}"></span> </p> </blockquote> <p>Donde: </p> <dl><dd><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 {\begin{matrix}u_{1}:=u_{x}&u_{2}:=u_{y}&u_{3}:=u_{z}\\x_{1}:=x&x_{2}:=y&x_{3}:=z\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>:=</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>:=</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>:=</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>:=</mo> <mi>x</mi> </mtd> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>:=</mo> <mi>y</mi> </mtd> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>:=</mo> <mi>z</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}u_{1}:=u_{x}&u_{2}:=u_{y}&u_{3}:=u_{z}\\x_{1}:=x&x_{2}:=y&x_{3}:=z\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20c048843bf43f115f40da787e9e194a5ccb1eb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.997ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}u_{1}:=u_{x}&u_{2}:=u_{y}&u_{3}:=u_{z}\\x_{1}:=x&x_{2}:=y&x_{3}:=z\end{matrix}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit&section=4" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Velocidad" title="Velocidad">Velocidad</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Desplazamiento_(vector)&action=edit&section=5" title="Editar sección: Bibliografía"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Landau & Lifshitz: <i>Mecánica</i> (vol. 1), Ed. Reverté, Barcelona, 1991. <a href="/wiki/Especial:FuentesDeLibros/8429140816" class="internal mw-magiclink-isbn">ISBN 84-291-4081-6</a>.</li> <li>Landau & Lifshitz: <i>Teoría de la elasticidad</i> (vol. 7), Ed. Reverté, Barcelona, 1991.</li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.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-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; 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