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[o]" accesskey="o" class=""><span>Logga in</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="Fler alternativ" > <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="Personliga verktyg" > <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">Personliga verktyg</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Användarmeny" > <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_sv.wikipedia.org&uselang=sv"><span>Stöd Wikipedia</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Skapa_konto&returnto=Trajektoria" title="Du uppmuntras att skapa ett konto och logga in, men det är inte obligatoriskt"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Skapa konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Inloggning&returnto=Trajektoria" title="Inloggning ger tillgång till fler funktioner för den som vill skriva och redigera artiklar. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logga in</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"> Sidor för utloggade redigerare <a href="/wiki/Hj%C3%A4lp:Introduktion" aria-label="Läs mer om redigering"><span>läs mer</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/Special:Mina_bidrag" title="En lista över redigeringar från denna IP-adress [y]" accesskey="y"><span>Bidrag</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:Min_diskussion" title="Diskussion om redigeringar från det här IP-numret [n]" accesskey="n"><span>Diskussion</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="Webbplats"> <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="Innehåll" 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">Innehåll</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</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">Inledning</div> </a> </li> <li id="toc-Trajektorians_fysik" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trajektorians_fysik"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Trajektorians fysik</span> </div> </a> <ul id="toc-Trajektorians_fysik-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Källor" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Källor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Källor</span> </div> </a> <ul id="toc-Källor-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="Innehåll" 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="Växla innehållsförteckningen" > <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">Växla innehållsförteckningen</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">Trajektoria</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="Gå till en artikel på ett annat språk. Tillgänglig på 50 språk" > <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-50" 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">50 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%B1" title="مسار – arabiska" lang="ar" hreflang="ar" data-title="مسار" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%9E%E0%A7%8D%E0%A6%9A%E0%A6%BE%E0%A6%B0%E0%A6%AA%E0%A6%A5" title="সঞ্চারপথ – bengali" lang="bn" hreflang="bn" data-title="সঞ্চারপথ" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D1%8B%D1%8F" title="Траекторыя – belarusiska" lang="be" hreflang="be" data-title="Траекторыя" data-language-autonym="Беларуская" data-language-local-name="belarusiska" 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%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D1%8B%D1%8F" title="Траекторыя – belarusiska (tarasjkevitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Траекторыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusiska (tarasjkevitsa)" 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%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%8F" title="Траектория – bulgariska" lang="bg" hreflang="bg" data-title="Траектория" data-language-autonym="Български" data-language-local-name="bulgariska" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Vertikalni_hitac" title="Vertikalni hitac – bosniska" lang="bs" hreflang="bs" data-title="Vertikalni hitac" data-language-autonym="Bosanski" data-language-local-name="bosniska" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Traject%C3%B2ria_(cinem%C3%A0tica)" title="Trajectòria (cinemàtica) – katalanska" lang="ca" hreflang="ca" data-title="Trajectòria (cinemàtica)" data-language-autonym="Català" data-language-local-name="katalanska" 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%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Траектори – tjuvasjiska" lang="cv" hreflang="cv" data-title="Траектори" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjiska" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Trajektorie" title="Trajektorie – tjeckiska" lang="cs" hreflang="cs" data-title="Trajektorie" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Trajektorie_(Physik)" title="Trajektorie (Physik) – tyska" lang="de" hreflang="de" data-title="Trajektorie (Physik)" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Trajektoor" title="Trajektoor – estniska" lang="et" hreflang="et" data-title="Trajektoor" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%BF%CF%87%CE%B9%CE%AC" title="Τροχιά – grekiska" lang="el" hreflang="el" data-title="Τροχιά" data-language-autonym="Ελληνικά" data-language-local-name="grekiska" 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/Trajectory" title="Trajectory – engelska" lang="en" hreflang="en" data-title="Trajectory" data-language-autonym="English" data-language-local-name="engelska" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Trayectoria" title="Trayectoria – spanska" lang="es" hreflang="es" data-title="Trayectoria" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Trajektorio" title="Trajektorio – esperanto" lang="eo" hreflang="eo" data-title="Trajektorio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ibilbide_(fisika)" title="Ibilbide (fisika) – baskiska" lang="eu" hreflang="eu" data-title="Ibilbide (fisika)" data-language-autonym="Euskara" data-language-local-name="baskiska" 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/%D9%85%D8%B3%DB%8C%D8%B1_%D9%BE%DB%8C%D9%85%D8%A7%DB%8C%D8%B4" title="مسیر پیمایش – persiska" lang="fa" hreflang="fa" data-title="مسیر پیمایش" data-language-autonym="فارسی" data-language-local-name="persiska" 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/Trajectoire" title="Trajectoire – franska" lang="fr" hreflang="fr" data-title="Trajectoire" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D5%BF%D5%A1%D5%A3%D5%AB%D5%AE" title="Հետագիծ – armeniska" lang="hy" hreflang="hy" data-title="Հետագիծ" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Okomiti_hitac" title="Okomiti hitac – kroatiska" lang="hr" hreflang="hr" data-title="Okomiti hitac" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Trajektorio" title="Trajektorio – ido" lang="io" hreflang="io" data-title="Trajektorio" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Lintasan" title="Lintasan – indonesiska" lang="id" hreflang="id" data-title="Lintasan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" 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/Traiettoria" title="Traiettoria – italienska" lang="it" hreflang="it" data-title="Traiettoria" data-language-autonym="Italiano" data-language-local-name="italienska" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%9C%D7%95%D7%9C_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="מסלול (פיזיקה) – hebreiska" lang="he" hreflang="he" data-title="מסלול (פיזיקה)" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%8F" title="Траектория – kazakiska" lang="kk" hreflang="kk" data-title="Траектория" data-language-autonym="Қазақша" data-language-local-name="kazakiska" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Trajektwa" title="Trajektwa – haitiska" lang="ht" hreflang="ht" data-title="Trajektwa" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiska" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%8F" title="Траектория – kirgiziska" lang="ky" hreflang="ky" data-title="Траектория" data-language-autonym="Кыргызча" data-language-local-name="kirgiziska" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Trajektorija" title="Trajektorija – lettiska" lang="lv" hreflang="lv" data-title="Trajektorija" data-language-autonym="Latviešu" data-language-local-name="lettiska" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Trajektorija" title="Trajektorija – litauiska" lang="lt" hreflang="lt" data-title="Trajektorija" data-language-autonym="Lietuvių" data-language-local-name="litauiska" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/P%C3%A1lya_(fizika)" title="Pálya (fizika) – ungerska" lang="hu" hreflang="hu" data-title="Pálya (fizika)" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%98%D0%B0" title="Траекторија – makedonska" lang="mk" hreflang="mk" data-title="Траекторија" data-language-autonym="Македонски" data-language-local-name="makedonska" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Traject" title="Traject – nederländska" lang="nl" hreflang="nl" data-title="Traject" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BC%BE%E9%81%93" title="弾道 – japanska" lang="ja" hreflang="ja" data-title="弾道" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Trayektoriya" title="Trayektoriya – uzbekiska" lang="uz" hreflang="uz" data-title="Trayektoriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekiska" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tor_ruchu" title="Tor ruchu – polska" lang="pl" hreflang="pl" data-title="Tor ruchu" data-language-autonym="Polski" data-language-local-name="polska" 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/Trajet%C3%B3ria" title="Trajetória – portugisiska" lang="pt" hreflang="pt" data-title="Trajetória" data-language-autonym="Português" data-language-local-name="portugisiska" 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/Traiectorie" title="Traiectorie – rumänska" lang="ro" hreflang="ro" data-title="Traiectorie" data-language-autonym="Română" data-language-local-name="rumänska" 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%A2%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%8F" title="Траектория – ryska" lang="ru" hreflang="ru" data-title="Траектория" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Trajektorja" title="Trajektorja – albanska" lang="sq" hreflang="sq" data-title="Trajektorja" data-language-autonym="Shqip" data-language-local-name="albanska" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Trajectory" title="Trajectory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Trajectory" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Trajekt%C3%B3ria_(krivka)" title="Trajektória (krivka) – slovakiska" lang="sk" hreflang="sk" data-title="Trajektória (krivka)" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pot" title="Pot – slovenska" lang="sl" hreflang="sl" data-title="Pot" data-language-autonym="Slovenščina" data-language-local-name="slovenska" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%DB%8E%D8%A8%D8%A7%D8%B2%DA%AF%DB%95" title="ڕێبازگە – centralkurdiska" lang="ckb" hreflang="ckb" data-title="ڕێبازگە" data-language-autonym="کوردی" data-language-local-name="centralkurdiska" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%83%D1%82%D0%B0%D1%9A%D0%B0" title="Путања – serbiska" lang="sr" hreflang="sr" data-title="Путања" data-language-autonym="Српски / srpski" 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href="https://www.wikidata.org/wiki/Special:EntityPage/Q193139" title="Länk till anslutet databasobjekt [g]" accesskey="g"><span>Wikidata-objekt</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="Sidverktyg"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <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">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">dölj</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">Från Wikipedia</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="sv" dir="ltr"><p><b>Trajektoria</b> betecknar den bana i vilken en partikel rör sig i t. ex. en sjö eller i atmosfären. Genom beräkning av trajektorier kan man t. ex. följa föroreningars spridning i vatten och luft. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:RiflemansRule.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/RiflemansRule.svg/300px-RiflemansRule.svg.png" decoding="async" width="300" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/RiflemansRule.svg/450px-RiflemansRule.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/RiflemansRule.svg/600px-RiflemansRule.svg.png 2x" data-file-width="668" data-file-height="369" /></a><figcaption>llustration som visar banan för en kula som avfyras mot ett mål i en uppförsbacke.</figcaption></figure> <p>Ett rörligt föremål kan vara en <a href="/wiki/Projektil" title="Projektil">projektil</a> eller en <a href="/wiki/Satellit" title="Satellit">satellit</a>. Till exempel kan också vara en planetbana, en <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> eller en <a href="/wiki/Komet" title="Komet">komet</a> som rör sig runt en central massa. En bana kan beskrivas matematiskt antingen genom geometrin hos banan, eller som positionen för det rörliga objektet över tiden. </p><p>I reglerteknik är en bana i tiden ordnad uppsättning av tillstånd i ett dynamiskt system. I diskret matematik, är en bana en sekvens <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 (f^{k}(x))_{k\in \mathbb {N} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (f^{k}(x))_{k\in \mathbb {N} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73d2c9caf41f19d3acad170d9b8c3029aae29067" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.729ex; height:3.176ex;" alt="{\displaystyle (f^{k}(x))_{k\in \mathbb {N} }}"></span> av värden som räknats fram genom itererad tillämpning av en kartläggning <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> för ett element <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> från dess källa. </p> <div class="mw-heading mw-heading2"><h2 id="Trajektorians_fysik">Trajektorians fysik</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajektoria&veaction=edit&section=1" title="Redigera avsnitt: Trajektorians fysik" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajektoria&action=edit&section=1" title="Redigera avsnitts källkod: Trajektorians fysik"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ett välkänt exempel på en bana är banan för en projektil, såsom en kastad boll eller en gunga. I en mycket förenklad modell rör sig objektet enbart genom påverkan av ett likformigt <a href="/wiki/Gravitationskraft" class="mw-redirect" title="Gravitationskraft">gravitationskraftfält</a>. Detta kan vara en god approximation för en sten som kastas en kortare sträcka, t.ex., vid ytan av månen. I denna enkla approximation, tar banan formen av en <a href="/wiki/Parabel_(kurva)" title="Parabel (kurva)">parabel</a>. Generellt vid fastställandet av banor kan det vara nödvändigt att ta hänsyn till olikformiga gravitationskrafter och <a href="/wiki/Luftmotst%C3%A5nd" title="Luftmotstånd">luftmotstånd</a> (drift och <a href="/wiki/Aerodynamik" title="Aerodynamik">aerodynamik</a>). Detta är centralt för disciplinen <a href="/wiki/Ballistik" title="Ballistik">ballistik</a>. </p><p>Ett av de viktiga resultaten av <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newtons</a> mekanik var möjligheten att härleda <a href="/wiki/Keplers_lagar" title="Keplers lagar">Keplers lagar</a>. I <a href="/wiki/Gravitationsf%C3%A4lt" class="mw-redirect" title="Gravitationsfält">gravitationsfältet</a> hos en masspunkt eller en sfäriskt symmetrisk utbredd massa (t.ex. <a href="/wiki/Solen" title="Solen">solen</a>), är banan för ett rörligt föremål en <a href="/wiki/Konisk_sektion" class="mw-redirect" title="Konisk sektion">konisk sektion</a>, vanligtvis en <a href="/wiki/Ellips_(matematik)" title="Ellips (matematik)">ellips</a> eller en <a href="/wiki/Hyperbel" title="Hyperbel">hyperbel</a>. Detta överensstämmer med observerade banorna hos planeter, kometer och konstgjorda rymdfarkoster som en tämligen bra approximation, även för en komet som passerar nära solen, då den också påverkas av andra krafter, såsom solvinden och strålningstryck, som modifierar dess bana, och orsakar att kometen matar ut material i rymden. </p><p>Newtons teori utvecklades senare till den gren av <a href="/wiki/Teoretisk_fysik" title="Teoretisk fysik">teoretisk fysik</a> som kallas klassisk mekanik. Den utnyttjar matematikerna <a href="/wiki/Differentialkalkyl" title="Differentialkalkyl">differentialkalkyl</a> (som de facto också initierats av Newton i hans ungdom). Under århundraden, har otaliga forskare bidragit till utvecklingen av dessa två discipliner. Klassisk mekanik blev den mest framträdande demonstrationen av kraften i rationellt tänkande i vetenskap och teknik. Den hjälper till att förstå och förutsäga ett stort antal olika av fenomen varav banor bara är ett exempel. </p><p>Betrakta en partikel av massa <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>, som rör sig i ett potentialfält <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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span>. Fysiskt sett representerar massan tröghet, och fältet <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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> representerar externa krafter, av en viss typ känd som kallas "konservativ". Det vill säga, givet på varje relevanta position, finns det ett sätt att bestämma den associerade kraft som skulle verka i denna position, säg från tyngdkraften. Alla krafter kan dock inte uttryckas på detta sätt. </p><p>Rörelsen hos partikeln beskrivs av en andra ordningens differentialekvation </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 m{\frac {\mathrm {d} ^{2}{\vec {x}}(t)}{\mathrm {d} t^{2}}}=-\nabla V({\vec {x}}(t))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∇</mi> <mi>V</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m{\frac {\mathrm {d} ^{2}{\vec {x}}(t)}{\mathrm {d} t^{2}}}=-\nabla V({\vec {x}}(t))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/963831409533ffb8fae5f225cb69e2cc8c28f4ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.619ex; height:6.343ex;" alt="{\displaystyle m{\frac {\mathrm {d} ^{2}{\vec {x}}(t)}{\mathrm {d} t^{2}}}=-\nabla V({\vec {x}}(t))}"></span> with <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 {\vec {x}}=(x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {x}}=(x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ecdc4cb0c225b2fdf59c9107da4a83004d7d007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.879ex; height:2.843ex;" alt="{\displaystyle {\vec {x}}=(x,y,z)}"></span></dd></dl> <p>På den högra sidan, är den kraft som ges i form av <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 \nabla V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1dd574e7657477e8993428d3a9238f919323f4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.723ex; height:2.176ex;" alt="{\displaystyle \nabla V}"></span>, gradienten av potentialen, tagen vid lägen längs banan. Detta är den matematiska formen av <a href="/wiki/Newtons_andra_r%C3%B6relselag" class="mw-redirect" title="Newtons andra rörelselag">Newtons andra rörelselag</a>: kraften är lika med massan gånger acceleration, för sådana situationer. </p> <div class="mw-heading mw-heading2"><h2 id="Källor"><span id="K.C3.A4llor"></span>Källor</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajektoria&veaction=edit&section=2" title="Redigera avsnitt: Källor" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajektoria&action=edit&section=2" title="Redigera avsnitts källkod: Källor"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="plainlinks"><i>Den här artikeln är helt eller delvis baserad på material från <a class="external text" href="https://en.wikipedia.org/wiki/Main_Page">engelskspråkiga Wikipedia</a>, <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Trajectory&oldid=707275466">tidigare version</a>.</i></span></dd></dl> <ul><li><a href="/wiki/Bra_B%C3%B6ckers_lexikon" title="Bra Böckers lexikon">Bra Böckers lexikon</a>, 1980.</li></ul> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output link+table.navbox{margin-top:-1px}.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow,.mw-parser-output table.navbox th{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-thlinkcolor .navbox-title button,.mw-parser-output .navbox-thlinkcolor .navbox-title .mw-collapsible-text,.mw-parser-output .navbox-thlinkcolor .navbox-title a{color:inherit}.mw-parser-output .nowraplinks a,.mw-parser-output .nowraplinks .selflink{white-space:nowrap}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right;font-weight:bold;padding-left:1em;padding-right:1em}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-title,.mw-parser-output table.navbox th{background:#b0c4de}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background:#d0e0f5}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background:#deeafa}.mw-parser-output .navbox-even{background:#f7f7f7}.mw-parser-output .navbox-odd{background:transparent}</style><table cellspacing="0" class="navbox" style="border-spacing:0;"><tbody><tr><td style="padding:2px;"><table cellspacing="0" class="nowraplinks hlist auktoritetsdata navbox-inner" style="border-spacing:0;background:transparent;color:inherit;"><tbody><tr><th scope="row" class="navbox-group"><a href="/wiki/Auktoritetsdata" title="Auktoritetsdata">Auktoritetsdata</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px;"><div style="padding:0em 0.25em;"> • <a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/subjects/sh2005004313">sh2005004313</a></span> • <a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4208631-0">4208631-0</a></span> • <a href="/wiki/Tjeckiska_nationalbiblioteket" title="Tjeckiska nationalbiblioteket">NKC</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph644351&CON_LNG=ENG">ph644351</a></span></div></td></tr></tbody></table></td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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