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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="Vietne"> <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="Saturs" 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">Saturs</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">pārvietot uz sānjoslu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">paslēpt</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">Sākums</div> </a> </li> <li id="toc-Ņūtona_likumi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ņūtona_likumi"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Ņūtona likumi</span> </div> </a> <ul id="toc-Ņūtona_likumi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mehāniska_sistēma" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mehāniska_sistēma"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Mehāniska sistēma</span> </div> </a> <ul id="toc-Mehāniska_sistēma-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Absolūti_cieta_ķermeņa_dinamika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Absolūti_cieta_ķermeņa_dinamika"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Absolūti cieta ķermeņa dinamika</span> </div> </a> <ul id="toc-Absolūti_cieta_ķermeņa_dinamika-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="Saturs" 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="Pārslēgt satura rādītāju" > <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">Pārslēgt satura rādītāju</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">Dinamika (mehānika)</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="Pāriet uz rakstu citā valodā. Pieejams 75 valodās" > <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-75" 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">75 valodas</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/%D8%B9%D9%84%D9%85_%D8%A7%D9%84%D8%AA%D8%AD%D8%B1%D9%8A%D9%83" title="علم التحريك – arābu" lang="ar" hreflang="ar" data-title="علم التحريك" data-language-autonym="العربية" data-language-local-name="arābu" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Din%C3%A1mica_(mec%C3%A1nica)" title="Dinámica (mecánica) – astūriešu" lang="ast" hreflang="ast" data-title="Dinámica (mecánica)" data-language-autonym="Asturianu" data-language-local-name="astūriešu" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Dinamika" title="Dinamika – azerbaidžāņu" lang="az" hreflang="az" data-title="Dinamika" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaidžāņu" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9_(%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9)" title="دینامیک (مکانیک) – South Azerbaijani" lang="azb" hreflang="azb" data-title="دینامیک (مکانیک)" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Дынаміка – baltkrievu" lang="be" hreflang="be" data-title="Дынаміка" data-language-autonym="Беларуская" data-language-local-name="baltkrievu" 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%94%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Дынаміка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Дынаміка" 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%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Динамика – bulgāru" lang="bg" hreflang="bg" data-title="Динамика" data-language-autonym="Български" data-language-local-name="bulgāru" 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%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="গতিবিদ্যা – bengāļu" lang="bn" hreflang="bn" data-title="গতিবিদ্যা" data-language-autonym="বাংলা" data-language-local-name="bengāļu" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Dinamika" title="Dinamika – bosniešu" lang="bs" hreflang="bs" data-title="Dinamika" data-language-autonym="Bosanski" data-language-local-name="bosniešu" 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/Din%C3%A0mica" title="Dinàmica – katalāņu" lang="ca" hreflang="ca" data-title="Dinàmica" data-language-autonym="Català" data-language-local-name="katalāņu" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9_(%D9%85%DB%8C%DA%A9%D8%A7%D9%86%DB%8C%DA%A9)" title="دینامیک (میکانیک) – centrālkurdu" lang="ckb" hreflang="ckb" data-title="دینامیک (میکانیک)" data-language-autonym="کوردی" data-language-local-name="centrālkurdu" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Dynamika" title="Dynamika – čehu" lang="cs" hreflang="cs" data-title="Dynamika" data-language-autonym="Čeština" data-language-local-name="čehu" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Динамика (физика) – čuvašu" lang="cv" hreflang="cv" data-title="Динамика (физика)" data-language-autonym="Чӑвашла" data-language-local-name="čuvašu" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Dynamik" title="Dynamik – dāņu" lang="da" hreflang="da" data-title="Dynamik" data-language-autonym="Dansk" data-language-local-name="dāņu" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dynamik_(Physik)" title="Dynamik (Physik) – vācu" lang="de" hreflang="de" data-title="Dynamik (Physik)" data-language-autonym="Deutsch" data-language-local-name="vācu" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE" title="Δυναμική – grieķu" lang="el" hreflang="el" data-title="Δυναμική" data-language-autonym="Ελληνικά" data-language-local-name="grieķu" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Dynamics_(mechanics)" title="Dynamics (mechanics) – angļu" lang="en" hreflang="en" data-title="Dynamics (mechanics)" data-language-autonym="English" data-language-local-name="angļu" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Dinamiko" title="Dinamiko – esperanto" lang="eo" hreflang="eo" data-title="Dinamiko" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Din%C3%A1mica" title="Dinámica – spāņu" lang="es" hreflang="es" data-title="Dinámica" data-language-autonym="Español" data-language-local-name="spāņu" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/D%C3%BCnaamika" title="Dünaamika – igauņu" lang="et" hreflang="et" data-title="Dünaamika" data-language-autonym="Eesti" data-language-local-name="igauņu" 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/Dinamika" title="Dinamika – basku" lang="eu" hreflang="eu" data-title="Dinamika" data-language-autonym="Euskara" data-language-local-name="basku" 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%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9" title="دینامیک – persiešu" lang="fa" hreflang="fa" data-title="دینامیک" data-language-autonym="فارسی" data-language-local-name="persiešu" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Dynamiikka" title="Dynamiikka – somu" lang="fi" hreflang="fi" data-title="Dynamiikka" data-language-autonym="Suomi" data-language-local-name="somu" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Dynamique_(m%C3%A9canique)" title="Dynamique (mécanique) – franču" lang="fr" hreflang="fr" data-title="Dynamique (mécanique)" data-language-autonym="Français" data-language-local-name="franču" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Dinimic" title="Dinimic – īru" lang="ga" hreflang="ga" data-title="Dinimic" data-language-autonym="Gaeilge" data-language-local-name="īru" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Din%C3%A1mica" title="Dinámica – galisiešu" lang="gl" hreflang="gl" data-title="Dinámica" data-language-autonym="Galego" data-language-local-name="galisiešu" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%93%D7%99%D7%A0%D7%9E%D7%99%D7%A7%D7%94_(%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%94)" title="דינמיקה (מכניקה) – ivrits" lang="he" hreflang="he" data-title="דינמיקה (מכניקה)" data-language-autonym="עברית" data-language-local-name="ivrits" 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%97%E0%A4%A4%E0%A4%BF_%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8" title="गति विज्ञान – hindi" lang="hi" hreflang="hi" data-title="गति विज्ञान" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Dinamika" title="Dinamika – horvātu" lang="hr" hreflang="hr" data-title="Dinamika" data-language-autonym="Hrvatski" data-language-local-name="horvātu" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Dinamik" title="Dinamik – haitiešu" lang="ht" hreflang="ht" data-title="Dinamik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiešu" 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/%D4%B4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1_(%D5%B4%D5%A5%D5%AD%D5%A1%D5%B6%D5%AB%D5%AF%D5%A1)" title="Դինամիկա (մեխանիկա) – armēņu" lang="hy" hreflang="hy" data-title="Դինամիկա (մեխանիկա)" data-language-autonym="Հայերեն" data-language-local-name="armēņu" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Dynamica" title="Dynamica – interlingva" lang="ia" hreflang="ia" data-title="Dynamica" data-language-autonym="Interlingua" data-language-local-name="interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Dinamika_(mekanika)" title="Dinamika (mekanika) – indonēziešu" lang="id" hreflang="id" data-title="Dinamika (mekanika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonēziešu" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Dinamiko" title="Dinamiko – ido" lang="io" hreflang="io" data-title="Dinamiko" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Dinamica" title="Dinamica – itāļu" lang="it" hreflang="it" data-title="Dinamica" data-language-autonym="Italiano" data-language-local-name="itāļu" 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%8B%95%E5%8A%9B%E5%AD%A6" title="動力学 – japāņu" lang="ja" hreflang="ja" data-title="動力学" data-language-autonym="日本語" data-language-local-name="japāņu" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90_(%E1%83%9B%E1%83%94%E1%83%A5%E1%83%90%E1%83%9C%E1%83%98%E1%83%99%E1%83%90)" title="დინამიკა (მექანიკა) – gruzīnu" lang="ka" hreflang="ka" data-title="დინამიკა (მექანიკა)" data-language-autonym="ქართული" data-language-local-name="gruzīnu" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Dinamika" title="Dinamika – karakalpaku" lang="kaa" hreflang="kaa" data-title="Dinamika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpaku" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Динамика – kazahu" lang="kk" hreflang="kk" data-title="Динамика" data-language-autonym="Қазақша" data-language-local-name="kazahu" 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%8F%99%EC%97%AD%ED%95%99" title="동역학 – korejiešu" lang="ko" hreflang="ko" data-title="동역학" data-language-autonym="한국어" data-language-local-name="korejiešu" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/D%C3%AEnam%C3%AEk" title="Dînamîk – kurdu" lang="ku" hreflang="ku" data-title="Dînamîk" data-language-autonym="Kurdî" data-language-local-name="kurdu" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D0%B4%D0%B0)" title="Динамика (механикада) – kirgīzu" lang="ky" hreflang="ky" data-title="Динамика (механикада)" data-language-autonym="Кыргызча" data-language-local-name="kirgīzu" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Dinamika_(mechanika)" title="Dinamika (mechanika) – lietuviešu" lang="lt" hreflang="lt" data-title="Dinamika (mechanika)" data-language-autonym="Lietuvių" data-language-local-name="lietuviešu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Динамика (физика) – maķedoniešu" lang="mk" hreflang="mk" data-title="Динамика (физика)" data-language-autonym="Македонски" data-language-local-name="maķedoniešu" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Dinamik" title="Dinamik – malajiešu" lang="ms" hreflang="ms" data-title="Dinamik" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiešu" 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%92%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%94%E1%80%99%E1%80%85%E1%80%BA" title="ဒိုင်းနမစ် – birmiešu" lang="my" hreflang="my" data-title="ဒိုင်းနမစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmiešu" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Dynamica" title="Dynamica – holandiešu" lang="nl" hreflang="nl" data-title="Dynamica" data-language-autonym="Nederlands" data-language-local-name="holandiešu" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Dynamikk_i_mekanikk" title="Dynamikk i mekanikk – jaunnorvēģu" lang="nn" hreflang="nn" data-title="Dynamikk i mekanikk" data-language-autonym="Norsk nynorsk" data-language-local-name="jaunnorvēģu" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Dynamikk_(mekanikk)" title="Dynamikk (mekanikk) – norvēģu bukmols" lang="nb" hreflang="nb" data-title="Dynamikk (mekanikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norvēģu bukmols" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A1%E0%A8%BE%E0%A8%87%E0%A8%A8%E0%A8%BE%E0%A8%AE%E0%A8%BF%E0%A8%95%E0%A8%B8" title="ਡਾਇਨਾਮਿਕਸ – pandžabu" lang="pa" hreflang="pa" data-title="ਡਾਇਨਾਮਿਕਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžabu" 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/Dynamika_(fizyka)" title="Dynamika (fizyka) – poļu" lang="pl" hreflang="pl" data-title="Dynamika (fizyka)" data-language-autonym="Polski" data-language-local-name="poļu" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Din%C3%A0mica" title="Dinàmica – Piedmontese" lang="pms" hreflang="pms" data-title="Dinàmica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Din%C3%A2mica" title="Dinâmica – portugāļu" lang="pt" hreflang="pt" data-title="Dinâmica" data-language-autonym="Português" data-language-local-name="portugāļu" 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/Dinamic%C4%83" title="Dinamică – rumāņu" lang="ro" hreflang="ro" data-title="Dinamică" data-language-autonym="Română" data-language-local-name="rumāņu" 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%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Динамика (физика) – krievu" lang="ru" hreflang="ru" data-title="Динамика (физика)" data-language-autonym="Русский" data-language-local-name="krievu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8%E0%A4%AE%E0%A5%8D" title="गतिविज्ञानम् – sanskrits" lang="sa" hreflang="sa" data-title="गतिविज्ञानम्" data-language-autonym="संस्कृतम्" data-language-local-name="sanskrits" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Dinamika_(fizika)" title="Dinamika (fizika) – serbu–horvātu" lang="sh" hreflang="sh" data-title="Dinamika (fizika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbu–horvātu" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80" title="ගති විද්‍යාව – singāļu" lang="si" hreflang="si" data-title="ගති විද්‍යාව" data-language-autonym="සිංහල" data-language-local-name="singāļu" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Dynamics" title="Dynamics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Dynamics" 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/Dynamika_(fyzika)" title="Dynamika (fyzika) – slovāku" lang="sk" hreflang="sk" data-title="Dynamika (fyzika)" data-language-autonym="Slovenčina" data-language-local-name="slovāku" 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/Dinamika" title="Dinamika – slovēņu" lang="sl" hreflang="sl" data-title="Dinamika" data-language-autonym="Slovenščina" data-language-local-name="slovēņu" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Dinamika" title="Dinamika – albāņu" lang="sq" hreflang="sq" data-title="Dinamika" data-language-autonym="Shqip" data-language-local-name="albāņu" 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%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Динамика (физика) – serbu" lang="sr" hreflang="sr" data-title="Динамика (физика)" data-language-autonym="Српски / srpski" data-language-local-name="serbu" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dynamik_(mekanik)" title="Dynamik (mekanik) – zviedru" lang="sv" hreflang="sv" data-title="Dynamik (mekanik)" data-language-autonym="Svenska" data-language-local-name="zviedru" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="இயக்கவியல் – tamilu" lang="ta" hreflang="ta" data-title="இயக்கவியல்" data-language-autonym="தமிழ்" data-language-local-name="tamilu" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="พลศาสตร์ – taju" lang="th" hreflang="th" data-title="พลศาสตร์" data-language-autonym="ไทย" data-language-local-name="taju" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Dinamik" title="Dinamik – turku" lang="tr" hreflang="tr" data-title="Dinamik" data-language-autonym="Türkçe" data-language-local-name="turku" 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%94%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Динаміка – ukraiņu" lang="uk" hreflang="uk" data-title="Динаміка" data-language-autonym="Українська" data-language-local-name="ukraiņu" 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/%D8%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA_(%D9%85%DB%8C%DA%A9%D8%A7%D9%86%DB%8C%D8%A7%D8%AA)" title="حرکیات (میکانیات) – urdu" lang="ur" hreflang="ur" data-title="حرکیات (میکانیات)" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99ng_l%E1%BB%B1c_h%E1%BB%8Dc" title="Động lực học – vjetnamiešu" lang="vi" hreflang="vi" data-title="Động lực học" data-language-autonym="Tiếng Việt" data-language-local-name="vjetnamiešu" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8A%A8%E5%8A%9B%E5%AD%A6" title="动力学 – vu ķīniešu" lang="wuu" hreflang="wuu" data-title="动力学" data-language-autonym="吴语" data-language-local-name="vu ķīniešu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%93%D7%99%D7%A0%D7%90%D7%9E%D7%99%D7%A7" title="דינאמיק – jidišs" lang="yi" hreflang="yi" data-title="דינאמיק" data-language-autonym="ייִדיש" data-language-local-name="jidišs" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8B%95%E5%8A%9B%E5%AD%B8" title="動力學 – ķīniešu" lang="zh" hreflang="zh" data-title="動力學" data-language-autonym="中文" data-language-local-name="ķīniešu" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C5%8Dng-le%CC%8Dk-ha%CC%8Dk" title="Tōng-le̍k-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Tōng-le̍k-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8B%95%E5%8A%9B%E5%AD%B8" title="動力學 – kantoniešu" lang="yue" hreflang="yue" data-title="動力學" data-language-autonym="粵語" data-language-local-name="kantoniešu" 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/Q128030#sitelinks-wikipedia" title="Labot starpvalodu saites" class="wbc-editpage">Labot saites</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q128030" title="Saistītais Vikidatu ieraksts [g]" accesskey="g"><span>Ieraksts Vikidatos</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="Lapas rīki"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izskats"> <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">Izskats</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">pārvietot uz sānjoslu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">paslēpt</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">Vikipēdijas lapa</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="lv" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Att%C4%93ls:Rownia_tarcie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Rownia_tarcie.svg/200px-Rownia_tarcie.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Rownia_tarcie.svg/300px-Rownia_tarcie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Rownia_tarcie.svg/400px-Rownia_tarcie.svg.png 2x" data-file-width="715" data-file-height="715" /></a><figcaption>Dinamikā pēta spēkus un ķermeņu mijiedarbību, kas izraisa kustību</figcaption></figure> <p><b>Dinamika</b> (no <a href="/wiki/Sengrie%C4%B7u_valoda" title="Sengrieķu valoda">sengrieķu</a> <i>δύναμις</i> — ‘spēks’) ir <a href="/wiki/Meh%C4%81nika" title="Mehānika">mehānikas</a> nozare, kas pēta <a href="/wiki/Fizik%C4%81ls_%C4%B7ermenis" title="Fizikāls ķermenis">ķermeņu</a> <a href="/wiki/Meh%C4%81nisk%C4%81_kust%C4%ABba" title="Mehāniskā kustība">kustību</a> un savstarpējo <a href="/wiki/Mijiedarb%C4%ABba" class="mw-redirect" title="Mijiedarbība">mijiedarbību</a> atkarībā no <a href="/wiki/Sp%C4%93ks" title="Spēks">spēku</a> iedarbības. Ķermeņu kustību, neņemot vērā spēkus, kas uz tiem iedarbojas, pēta <a href="/wiki/Kinem%C4%81tika" title="Kinemātika">kinemātikā</a>. <a href="/wiki/Klasisk%C4%81_meh%C4%81nika" title="Klasiskā mehānika">Klasiskās mehānikas</a> dinamika balstās uz trim <a href="/wiki/%C5%85%C5%ABtona_likumi" title="Ņūtona likumi">Ņūtona likumiem</a>, visi pārējie tās likumi tiek iegūti pēc Ņūtona likumiem un priekšstata par <a href="/wiki/Telpa" title="Telpa">telpas</a> un <a href="/wiki/Laiks" title="Laiks">laika</a> homogenitāti un telpas izotropiju. </p><p>Ķermeņa kustības raksturošanu, zinot, kādi spēki iedarbojas uz ķermeni, sauc par dinamikas galveno (tiešo, pirmo, pamata) uzdevumu. Spēku, kas darbojas uz ķermeni, noteikšanu, zinot ķermeņa kustību, sauc par apgriezto (otro) dinamikas uzdevumu. </p><p>Atkarībā no ķermeņiem un procesiem, kam tiek pievērsta uzmanība, dinamiku var iedalīt <a href="/wiki/Hidrodinamika" title="Hidrodinamika">hidrodinamikā</a>, <a href="/wiki/Elektrodinamika" title="Elektrodinamika">elektrodinamikā</a>, <a href="/wiki/Aerodinamika" title="Aerodinamika">aerodinamikā</a>, <a href="/wiki/Termodinamika" title="Termodinamika">termodinamika</a> un tā tālāk. </p> <div class="mw-heading mw-heading2"><h2 id="Ņūtona_likumi"><span id=".C5.85.C5.ABtona_likumi"></span>Ņūtona likumi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&veaction=edit&section=1" title="Labot sadaļu: Ņūtona likumi" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&action=edit&section=1" title="Labot sadaļas vikikodu: Ņūtona likumi"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Pamatraksts: <a href="/wiki/%C5%85%C5%ABtona_likumi" title="Ņūtona likumi">Ņūtona likumi</a></i> </p><p>Pirmais Ņūtona jeb <a href="/wiki/Inerce" title="Inerce">inerces</a> likums nosaka, ka ķermenis atrodas miera stāvoklī vai vienmērīgā taisnvirziena kustībā, ja uz to nedarbojas citi ķermeņi vai arī to iedarbības savstarpēji kompensējas. Ne visās atskaites sistēmās šis likums ir spēkā. Atskaites sistēmas, kurās Pirmais Ņūtona likums ir pareizs, sauc par inerciālām atskaites sistēmām, visas pārējās — par neinerciālām. Inerciālas atskaites sistēmas ir ķermeņi, kurus neietekmē citu ķermeņu iedarbība, kas varētu izraisīt <a href="/wiki/Pa%C4%81trin%C4%81jums" title="Paātrinājums">paātrinājumu</a>. </p><p>Otrais Ņūtona likums jeb <a href="/wiki/Materi%C4%81ls_punkts" title="Materiāls punkts">materiāla punkta</a> kustības dinamikas pamatlikums: inerciālā atskaites sistēmā ķermeņa paātrinājums <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 {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/546e6615827e17295718741fd0b86f639a947f16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:2.343ex;" alt="{\displaystyle {\vec {a}}}"></span> ir tieši <a href="/w/index.php?title=Proporcija&action=edit&redlink=1" class="new" title="Proporcija (vēl nav uzrakstīts)">proporcionāls</a> spēkam <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 {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span>, kas darbojas uz ķermeni, apgriezti proporcionāls ķermeņa <a href="/wiki/Masa" title="Masa">masai</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 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> un vērsts spēka darbības virzienā: </p><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 {\vec {a}}={\frac {\vec {F}}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a}}={\frac {\vec {F}}{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/983a50038e145f4b162f376015be06494b0186b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.205ex; height:6.009ex;" alt="{\displaystyle {\vec {a}}={\frac {\vec {F}}{m}}}"></span>. </p><p>Trešais Ņūtona jeb darbības un pretdarbības likums: divu ķermeņu mijiedarbības spēkiem ir vienādi <a href="/wiki/Absol%C5%ABt%C4%81_v%C4%93rt%C4%ABba" title="Absolūtā vērtība">moduļi</a> un pretēji vērsumi: </p><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 F_{12}=-F_{21}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{12}=-F_{21}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88a3b5533781cfd55e849c1fe83c0eb5c1c922b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.648ex; height:2.509ex;" alt="{\displaystyle F_{12}=-F_{21}}"></span>, </p><p>kur <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_{12}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{12}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35bd8bf2dd739f74f6c888ae839d364d7ca8cf8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.371ex; height:2.509ex;" alt="{\displaystyle F_{12}}"></span> ir spēks, ar kuru ķermenis 2 darbojas uz ķermeni 1, un <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_{21}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{21}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcfa9608168c7a364f4b08148b40189b4058f1c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.371ex; height:2.509ex;" alt="{\displaystyle F_{21}}"></span> ir spēks, ar kuru ķermenis 1 darbojas uz ķermeni 2. </p> <div class="mw-heading mw-heading2"><h2 id="Mehāniska_sistēma"><span id="Meh.C4.81niska_sist.C4.93ma"></span>Mehāniska sistēma</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&veaction=edit&section=2" title="Labot sadaļu: Mehāniska sistēma" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&action=edit&section=2" title="Labot sadaļas vikikodu: Mehāniska sistēma"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mehāniska sistēma ir materiālu punktu kopa, kurā notiek mehāniska mijiedarbība. Šādā izraudzītā sistēmā ietvertie materiālie punkti var veidot vienu vai vairākus atsevišķus fizikālus ķermeņus. Spēkus, kas darbojas starp sistēmā esošajiem materiālajiem punktiem, sauc par iekšējiem spēkiem <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 {f}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>f</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {f}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2c36da6dad4ad8949b0f84bbaf0b5cb6d811fe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.665ex; height:3.343ex;" alt="{\displaystyle {\vec {f}}}"></span>, bet spēkus, ar kuriem uz sistēmā ietilpstošajiem materiālajiem punktiem iedarbojas citi ķermeņi vai punkti, sauc par ārējiem spēkiem <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 {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span>. Ja uz sistēmu nedarbojas ārēki spēki, to sauc par <a href="/wiki/Nosl%C4%93gta_sist%C4%93ma" title="Noslēgta sistēma">noslēgtu sistēmu</a>. </p><p>Ja sistēmā darbojas tikai <a href="/wiki/Konservat%C4%ABvais_sp%C4%93ks" title="Konservatīvais spēks">konservatīvie spēki</a>, to sauc par konservatīvu sistēmu un tās pilnā <a href="/wiki/Meh%C4%81nisk%C4%81_ener%C4%A3ija" title="Mehāniskā enerģija">mehāniskā enerģija</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 W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> ir nemainīga: </p><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 W=W_{p}+W_{k}=const}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=W_{p}+W_{k}=const}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d31c51570bada606e15f61d66983d733a7ebda31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.467ex; height:2.843ex;" alt="{\displaystyle W=W_{p}+W_{k}=const}"></span>, </p><p>kur <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 W_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8daa318a0c0f1dcb48604b379590d72c7392c615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.253ex; height:2.843ex;" alt="{\displaystyle W_{p}}"></span> ir <a href="/wiki/Potenci%C4%81l%C4%81_ener%C4%A3ija" title="Potenciālā enerģija">potenciālā enerģija</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 W_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aea7ab451421a62d7de329faed9aa86419bebeab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.282ex; height:2.509ex;" alt="{\displaystyle W_{k}}"></span> ir <a href="/wiki/Kin%C4%93tisk%C4%81_ener%C4%A3ija" title="Kinētiskā enerģija">kinētiskā enerģija</a>. </p><p>Ja sistēmā darbojas arī <a href="/w/index.php?title=Disipat%C4%ABvais_sp%C4%93ks&action=edit&redlink=1" class="new" title="Disipatīvais spēks (vēl nav uzrakstīts)">disipatīvie (nekonservatīvie) spēki</a>, to sauc par disipatīvu sistēmu un tās pilnā mehāniskā enerģija samazinās (enerģijas disipācija). Visas reālas mehāniskās sistēmas ir disipatīvas (tajās darbojas, piemēram, <a href="/wiki/Berzes_sp%C4%93ks" class="mw-redirect" title="Berzes spēks">berzes spēki</a>), taču, ja disipatīvie spēki ir mazi, tos var neievērot un lietot <a href="/wiki/Ener%C4%A3ijas_nez%C5%ABdam%C4%ABbas_likums" title="Enerģijas nezūdamības likums">enerģijas nezūdamības likumu</a> kā šai mehāniskajai sistēmai pilnībā atbilstošu. </p><p>Lai raksturotu mehānisku sistēmu, parasti izmanto masas (inerces) centra jēdzienu. <a href="/wiki/Masas_centrs" title="Masas centrs">Masas centrs</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 C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> ir punkts, kura stāvokli <a href="/wiki/Koordin%C4%81tu_sist%C4%93ma" title="Koordinātu sistēma">koordinātu sistēmā</a> nosaka no atsevišķo punktu masām <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_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.84ex; height:2.009ex;" alt="{\displaystyle m_{i}}"></span> un to <a href="/w/index.php?title=R%C4%81diusvektors&action=edit&redlink=1" class="new" title="Rādiusvektors (vēl nav uzrakstīts)">rādiusvektoriem</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 {\vec {r_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8aad177c5c2e4fd39ba2400511e620863b425552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.324ex; height:3.343ex;" alt="{\displaystyle {\vec {r_{i}}}}"></span> atkarīgs rādiusvektors <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 {r_{C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r_{C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0df72a2e7b47d405a544810292447fa942a1dc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.53ex; height:3.343ex;" alt="{\displaystyle {\vec {r_{C}}}}"></span>: </p><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 {\vec {r_{C}}}={\frac {1}{m}}\sum _{i=1}^{N}m_{i}{\vec {r_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>m</mi> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r_{C}}}={\frac {1}{m}}\sum _{i=1}^{N}m_{i}{\vec {r_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e34feb75e66bfe018d07c0b82e06aeebf8fd4ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:17.798ex; height:7.343ex;" alt="{\displaystyle {\vec {r_{C}}}={\frac {1}{m}}\sum _{i=1}^{N}m_{i}{\vec {r_{i}}}}"></span>, </p><p>kur <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> ir sistēmas kopējā masa, <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> — materiālu punktu skaits. </p><p>Par smaguma centru sauc punktu, kurā pielikts sistēmas <a href="/wiki/Smaguma_sp%C4%93ks" title="Smaguma spēks">smaguma spēks</a>, kas ir visu sistēmas sastāvdaļu smaguma spēku kopspēks. Viendabīgā smaguma spēku <a href="/wiki/Lauks_(fizika)" title="Lauks (fizika)">laukā</a> smaguma centrs sakrīt ar masas centru. Masas centrs sistēmai piemīt vienmēr atšķirībā no smaguma centra, kura var arī nebūt. </p><p>Mehāniskai sistēmai piemīt <a href="/wiki/Impulss" title="Impulss">impulss</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 {\vec {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fee53c81592db54e0fe6c6f9eba002bb1dc74b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.415ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}}"></span>, kurš vienāds ar sistēmas visu materiālo punktu impulsu vektoriālo summu: </p><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 {\vec {p}}=\sum _{i=1}^{N}m_{i}{\vec {v_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}=\sum _{i=1}^{N}m_{i}{\vec {v_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d1cd7df210999df358c549604b84c9a8b18219d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.089ex; width:13.419ex; height:7.343ex;" alt="{\displaystyle {\vec {p}}=\sum _{i=1}^{N}m_{i}{\vec {v_{i}}}}"></span>. </p><p>Tāpat sistēmas impulss vienāds ar sistēmas masas un sistēmas masas centra kustības ātruma reizinājumu: </p><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 {\vec {p}}=m{\vec {v_{C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}=m{\vec {v_{C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75269f129ee6a789412816349e40d379099f9425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:9.162ex; height:3.343ex;" alt="{\displaystyle {\vec {p}}=m{\vec {v_{C}}}}"></span>. </p><p>Pēc Otrā Ņūtona likuma un ņemot vērā Trešo Ņūtona likumu, sistēmai atbilst vienādojums </p><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 {\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}={\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}={\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bdd2ae3b5f7a81e8251efbb17b7ddabc990c542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.323ex; height:5.676ex;" alt="{\displaystyle {\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}={\vec {F}}}"></span>, </p><p>no kura redzams, ka sistēmas impulsu var izmainīt tikai ārēji spēki. Saskaņā ar <a href="/w/index.php?title=Impulsa_nez%C5%ABdam%C4%ABbas_likums&action=edit&redlink=1" class="new" title="Impulsa nezūdamības likums (vēl nav uzrakstīts)">impulsa nezūdamības likumu</a> noslēgtas sistēmas impulss ir nemainīgs. Savukārt, pēc impulsa projekcijas nezūdamības likuma, ja ārējā kopspēka projekcija kādā virzienā ir vienāda ar nulli, tad sistēmas impulsa projekcija šajā virzienā ir konstanta. </p><p>Tāpat, pēc Otrā Ņūtona likuma, </p><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 {\vec {a_{C}}}={\frac {\vec {F}}{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> <mi>m</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a_{C}}}={\frac {\vec {F}}{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98e30d10b4596a5065e48e99b4f61ad9b47732d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.686ex; height:6.009ex;" alt="{\displaystyle {\vec {a_{C}}}={\frac {\vec {F}}{m}}}"></span>, </p><p>kur <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 {a_{C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a_{C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a1a8bf372872241ae59aa1e300ac60a12bf27bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.711ex; height:3.343ex;" alt="{\displaystyle {\vec {a_{C}}}}"></span> ir sistēmas masas centra paātrinājums. </p><p>Tādējādi mehāniskas sistēmas masas centrs kustas kā materiāls punkts, kura masa ir vienāda ar sistēmas masu un uz kuru darbojas ar sistēmai pielikto kopspēku vienāds spēks. Ja sistēma ir <a href="/w/index.php?title=Absol%C5%ABti_ciets_%C4%B7ermenis&action=edit&redlink=1" class="new" title="Absolūti ciets ķermenis (vēl nav uzrakstīts)">absolūti ciets ķermenis</a>, kas atrodas <a href="/wiki/Virzes_kust%C4%ABba" title="Virzes kustība">virzes jeb translācijas kustībā</a>, tad visiem sistēmas materiālajiem punktiem ir vienāds paātrinājums. </p><p>Iespējams, ka sistēmas masa kustības laikā ir mainīga. Laika momentā <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 \operatorname {d} \!t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {d} \!t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ad7ee96be6eccc70d2c4e3a8d143406f64cc48a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.132ex; height:2.176ex;" alt="{\displaystyle \operatorname {d} \!t}"></span> ķermenim pievienojas vai no tā ātdalās daļiņas ar kopējo masu <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 \operatorname {d} \!m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {d} \!m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/845b42776f9a7a365bc0b3db533fc80015fc09f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.333ex; height:2.176ex;" alt="{\displaystyle \operatorname {d} \!m}"></span> un ātrumu <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 {v_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bd3de8e503f7274717139210b76ec8b64257acb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.324ex; height:3.343ex;" alt="{\displaystyle {\vec {v_{1}}}}"></span>. Šādu kustību raksturo mainīgas masas ķermeņa kustības dinamikas pamatvienādojums </p><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 {\frac {m\operatorname {d} \!{\vec {v}}}{\operatorname {d} \!t}}={\vec {F}}+{\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {m\operatorname {d} \!{\vec {v}}}{\operatorname {d} \!t}}={\vec {F}}+{\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16ddd068cb4e50e118fb9e48db7e0dda91799780" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.327ex; height:5.509ex;" alt="{\displaystyle {\frac {m\operatorname {d} \!{\vec {v}}}{\operatorname {d} \!t}}={\vec {F}}+{\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}"></span>, </p><p>kur <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 {u}}={\vec {v_{1}}}-{\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {u}}={\vec {v_{1}}}-{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e384f98fd114b16b1bf19af7945b9bc7107b5d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.768ex; height:3.343ex;" alt="{\displaystyle {\vec {u}}={\vec {v_{1}}}-{\vec {v}}}"></span> ir daļiņu relatīvais ātrums attiecībā pret ķermeni, bet <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 {\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10157f014f2f151af6d814ea1584f8421f61875c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:5.886ex; height:5.509ex;" alt="{\displaystyle {\frac {{\vec {u}}\operatorname {d} \!m}{\operatorname {d} \!t}}}"></span> ir <a href="/w/index.php?title=Reakcija_(meh%C4%81nika)&action=edit&redlink=1" class="new" title="Reakcija (mehānika) (vēl nav uzrakstīts)">reaktīvais spēks</a>. </p><p>Pēc tā iegūstams <a href="/w/index.php?title=Ciolkovska_vien%C4%81dojums&action=edit&redlink=1" class="new" title="Ciolkovska vienādojums (vēl nav uzrakstīts)">Ciolkovska vienādojums</a>, pēc kura var aprēķināt <a href="/wiki/Ra%C4%B7ete" title="Raķete">raķetes</a> attīstīto ātrumu, neņemot vērā Zemes <a href="/wiki/Smaguma_sp%C4%93ks" title="Smaguma spēks">pievilkšanas spēku</a> un <a href="/wiki/Aerodinamisk%C4%81_pretest%C4%ABba" title="Aerodinamiskā pretestība">gaisa pretestību</a>, </p><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 v=u\ln \left({\frac {m_{0}}{m}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>u</mi> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>m</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=u\ln \left({\frac {m_{0}}{m}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e68050564e8ed58ed5541013ac5e393e7de5779" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.588ex; height:4.843ex;" alt="{\displaystyle v=u\ln \left({\frac {m_{0}}{m}}\right)}"></span>, </p><p>kur <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6ff51ee949104fe6fae553cfbdfba29d5fac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{0}}"></span> ir raķetes palaišanas masa, <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> ir raķetes atlikusī masa. </p> <div class="mw-heading mw-heading2"><h2 id="Absolūti_cieta_ķermeņa_dinamika"><span id="Absol.C5.ABti_cieta_.C4.B7erme.C5.86a_dinamika"></span>Absolūti cieta ķermeņa dinamika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&veaction=edit&section=3" title="Labot sadaļu: Absolūti cieta ķermeņa dinamika" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dinamika_(meh%C4%81nika)&action=edit&section=3" title="Labot sadaļas vikikodu: Absolūti cieta ķermeņa dinamika"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Absolūti cieta ķermeņa kustības pamatveidi ir translācija jeb <a href="/wiki/Virzes_kust%C4%ABba" title="Virzes kustība">virzes kustība</a> un rotācija jeb <a href="/wiki/Griezes_kust%C4%ABba" title="Griezes kustība">griezes kustība</a>. Virzes kustībā visiem ķermeņa punktiem ir vienāds <a href="/wiki/P%C4%81rvietojums" title="Pārvietojums">pārvietojums</a>, <a href="/wiki/%C4%80trums" title="Ātrums">ātrums</a>, <a href="/wiki/Pa%C4%81trin%C4%81jums" title="Paātrinājums">paātrinājums</a>, tāpēc cieta ķermeņa translācijas dinamiku var reducēt uz <a href="/wiki/Materi%C4%81ls_punkts" title="Materiāls punkts">materiāla punkta</a> dinamiku. (Par materiāla punkta kustību skatīt: <a href="/wiki/Kinem%C4%81tika" title="Kinemātika">Kinemātika</a>.) </p> <table class="wikitable"> <caption>Virzes (translācijas) un griešanās (rotācijas) raksturlielumu līdzības </caption> <tbody><tr> <th>Virze </th> <th>Griešanās </th></tr> <tr> <td>noietais ceļš <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 l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span> </td> <td>pagrieziena leņķis <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> </td></tr> <tr> <td>lineārais ātrums <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 {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span> </td> <td>leņķiskais ātrums <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 {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4e066a68ceb355e3314fb2b97f1c0c421ca6074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:2.343ex;" alt="{\displaystyle {\vec {\omega }}}"></span> </td></tr> <tr> <td>lineārais tangenciālais paātrinājums <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 {a_{\tau }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {a_{\tau }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9069941e680dc8abbfaf590b64529f0e231bbe66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.324ex; height:3.343ex;" alt="{\displaystyle {\vec {a_{\tau }}}}"></span> </td> <td>leņķiskais paātrinājums <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 {\varepsilon }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ε</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\varepsilon }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/027c1af022c880c96e53b051d6675b2a6ff4d231" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.287ex; height:2.343ex;" alt="{\displaystyle {\vec {\varepsilon }}}"></span> </td></tr> <tr> <td>masa <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> </td> <td>inerces moments <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> </td></tr> <tr> <td>spēks <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 {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> </td> <td>spēka moments <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 {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b903a0e453efca49cfda6ba33edb465de21a6b1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.843ex;" alt="{\displaystyle {\vec {M}}}"></span> </td></tr> <tr> <td>vienmērīga kustība: <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 a_{\tau }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\tau }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9742a15cf5369a79cc4fada44f41b9717d30829f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.573ex; height:2.509ex;" alt="{\displaystyle a_{\tau }=0}"></span>, <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 l=vt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mi>v</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=vt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6548a58a66bb05a9217edfd4a71662fc3b260796" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.759ex; height:2.176ex;" alt="{\displaystyle l=vt}"></span> </p> </td> <td>vienmērīga kustība: <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 \varepsilon =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cbe653d369abd71fc0be98efbf59e9edc1bdfb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon =0}"></span>, <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 \varphi =\omega t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>=</mo> <mi>ω</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi =\omega t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4224e277c0ad8bc028bdc00fce8e2dd2227e075c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.904ex; height:2.509ex;" alt="{\displaystyle \varphi =\omega t}"></span> </p> </td></tr> <tr> <td>vienmērīgi mainīga kustība: <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 a_{\tau }=const}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{\tau }=const}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb68dbf76ce50abd7f3c1b32d695c72d93a1fa94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.87ex; height:2.343ex;" alt="{\displaystyle a_{\tau }=const}"></span>, <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=a_{\tau }t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </msub> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=a_{\tau }t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d35d4ac898d051ae9890501a97712c75091f27b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.378ex; height:2.343ex;" alt="{\displaystyle v=a_{\tau }t}"></span>, <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 l=v_{0}t+{\frac {a_{\tau }t^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </msub> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=v_{0}t+{\frac {a_{\tau }t^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/532497f648b848fef12398657ed7342dae09e801" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.696ex; height:5.676ex;" alt="{\displaystyle l=v_{0}t+{\frac {a_{\tau }t^{2}}{2}}}"></span> </p> </td> <td>vienmērīgi mainīga kustība: <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 \varepsilon =const}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon =const}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e85bee6b577dbc8d9d04936a50f201ddb825587" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.641ex; height:2.009ex;" alt="{\displaystyle \varepsilon =const}"></span>, <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 \omega =\varepsilon t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mi>ε</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =\varepsilon t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bf94fbf679dda30656dbefe9b36a03d37e8e02f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.467ex; height:2.009ex;" alt="{\displaystyle \omega =\varepsilon t}"></span>, <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 l=\omega _{0}t+{\frac {\varepsilon t^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ε</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=\omega _{0}t+{\frac {\varepsilon t^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb56ad35631fa15ad3a7c067c5e80c96f706a656" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.785ex; height:5.676ex;" alt="{\displaystyle l=\omega _{0}t+{\frac {\varepsilon t^{2}}{2}}}"></span> </p> </td></tr> <tr> <td>impulss <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 {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fee53c81592db54e0fe6c6f9eba002bb1dc74b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.415ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}}"></span> </td> <td>impulsa moments <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 {L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c139fc28d6ca3873993892f44e7331e5ff18fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.843ex;" alt="{\displaystyle {\vec {L}}}"></span> </td></tr> <tr> <td>kinētiskā enerģija <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 W_{k}={\frac {mv^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{k}={\frac {mv^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a1362bc9d1c2c2632412648c8994468be48b94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.439ex; height:5.676ex;" alt="{\displaystyle W_{k}={\frac {mv^{2}}{2}}}"></span> </td> <td>kinētiskā enerģija <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 W_{k}={\frac {I\omega ^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>I</mi> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{k}={\frac {I\omega ^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40d2b2344fe0d581ee7866d7ef3d7639ceecdb09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.889ex; height:5.676ex;" alt="{\displaystyle W_{k}={\frac {I\omega ^{2}}{2}}}"></span> </td></tr> <tr> <td>darbs <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 A=F_{l}l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=F_{l}l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55eeb9c52da3fc865ca0a885deb7d314f40b794c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.752ex; height:2.509ex;" alt="{\displaystyle A=F_{l}l}"></span> </td> <td>darbs <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 A=M\varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>M</mi> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=M\varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60765b938026cd9d9d20126cff56b44dc487b599" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.804ex; height:2.676ex;" alt="{\displaystyle A=M\varphi }"></span> </td></tr> <tr> <td>jauda <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 P={\vec {F}}{\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\vec {F}}{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcda88816f487ee6039b3cd2a1c87f2e41b01b5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.79ex; height:2.843ex;" alt="{\displaystyle P={\vec {F}}{\vec {v}}}"></span> </td> <td>jauda <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 P={\vec {M}}{\vec {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\vec {M}}{\vec {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/654b9f3bda81ee0a4815811fe2fca5ab1f7fc096" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.732ex; height:2.843ex;" alt="{\displaystyle P={\vec {M}}{\vec {\omega }}}"></span> </td></tr> <tr> <td>dinamikas pamatlikums <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 {F}}=m{\vec {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=m{\vec {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b202a8eaba4b424be52bcbaa043727b6ad9860" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.14ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}=m{\vec {a}}}"></span> vai <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 {F}}={\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}={\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2af930802998db59fac5f1cbf521f8cfae97c07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.323ex; height:5.676ex;" alt="{\displaystyle {\vec {F}}={\frac {\operatorname {d} \!{\vec {p}}}{\operatorname {d} \!t}}}"></span> </td> <td>dinamikas pamatlikums <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 {M}}=I{\vec {\varepsilon }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ε</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {M}}=I{\vec {\varepsilon }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec1998de9c9962bfae69ef53210c4e86baf949d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8ex; height:2.843ex;" alt="{\displaystyle {\vec {M}}=I{\vec {\varepsilon }}}"></span> vai <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 {M}}={\frac {\operatorname {d} \!{\vec {L}}}{\operatorname {d} \!t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {M}}={\frac {\operatorname {d} \!{\vec {L}}}{\operatorname {d} \!t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42da1b5780ffaa867061c3a519b3c7840e20e581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; 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