Jump to navigation Jump to search

General

Display information for equation id:math.870.7 on revision:870

* Page found: Hamiltonsches Prinzip (eq math.870.7)

(force rerendering)

Occurrences on the following pages:

Hash: 5ceb1b074967d14d2c9befac2cf90324

TeX (original user input):

S\left[ q \right]:=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{L\left( q,\dot{q},t \right)dt}

LaTeXML (experimental; uses MathML) rendering

MathML (6.106 KB / 1.164 KB) :

S [ q ] := t 1 t 2 L ( q , q ˙ , t ) 𝑑 t assign 𝑆 delimited-[] 𝑞 superscript subscript subscript 𝑡 1 subscript 𝑡 2 𝐿 𝑞 ˙ 𝑞 𝑡 differential-d 𝑡 {\displaystyle{\displaystyle S\left[q\right]:=\int\limits_{{{t}_{1}}}^{{{t}_{2% }}}{L\left(q,\dot{q},t\right)dt}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle S\left[q\right]:=\int\limits_{{{t}_{1}}}^{{{t}_{2%&#10;}}}{L\left(q,\dot{q},t\right)dt}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
      <mrow id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
        <mo id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml"></mo>
        <mrow id="p1.1.m1.1.20.1.2" xref="p1.1.m1.1.20.1.2.1.cmml">
          <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.20.1.2.1.1.cmml">[</mo>
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">q</mi>
          <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.20.1.2.1.1.cmml">]</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">:=</mo>
      <mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.20.2.1" xref="p1.1.m1.1.20.2.1.cmml">
          <munderover id="p1.1.m1.1.20.2.1a" xref="p1.1.m1.1.20.2.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml"></mo>
            <msub id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
              <mi id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml">t</mi>
              <mn id="p1.1.m1.1.8.1.2.1" xref="p1.1.m1.1.8.1.2.1.cmml">1</mn>
            </msub>
            <msub id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">
              <mi id="p1.1.m1.1.9.1.1" xref="p1.1.m1.1.9.1.1.cmml">t</mi>
              <mn id="p1.1.m1.1.9.1.2.1" xref="p1.1.m1.1.9.1.2.1.cmml">2</mn>
            </msub>
          </munderover>
        </mstyle>
        <mrow id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.20.2.2.cmml">
          <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">L</mi>
          <mo id="p1.1.m1.1.20.2.2.1" xref="p1.1.m1.1.20.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.20.2.2.2" xref="p1.1.m1.1.20.2.2.2.1.cmml">
            <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.20.2.2.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">q</mi>
            <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.20.2.2.2.1.cmml">,</mo>
            <mover accent="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
              <mi id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml">q</mi>
              <mo id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">˙</mo>
            </mover>
            <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.20.2.2.2.1.cmml">,</mo>
            <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">t</mi>
            <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.20.2.2.2.1.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.20.2.2.1a" xref="p1.1.m1.1.20.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.20.2.2.3" xref="p1.1.m1.1.20.2.2.3.cmml">
            <mo rspace="0pt" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">𝑑</mo>
            <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">t</mi>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
        <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">assign</csymbol>
        <apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
          <times id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑆</ci>
          <apply id="p1.1.m1.1.20.1.2.1.cmml" xref="p1.1.m1.1.20.1.2">
            <csymbol cd="latexml" id="p1.1.m1.1.20.1.2.1.1.cmml" xref="p1.1.m1.1.2">delimited-[]</csymbol>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑞</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">
          <apply id="p1.1.m1.1.20.2.1.cmml" xref="p1.1.m1.1.20.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.20.2.1.1.cmml" xref="p1.1.m1.1.20.2.1">superscript</csymbol>
            <apply id="p1.1.m1.1.20.2.1.2.cmml" xref="p1.1.m1.1.20.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.20.2.1.2.1.cmml" xref="p1.1.m1.1.20.2.1">subscript</csymbol>
              <int id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
              <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.8.1.3.cmml" xref="p1.1.m1.1.8.1">subscript</csymbol>
                <ci id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1">𝑡</ci>
                <cn type="integer" id="p1.1.m1.1.8.1.2.1.cmml" xref="p1.1.m1.1.8.1.2.1">1</cn>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.9.1.3.cmml" xref="p1.1.m1.1.9.1">subscript</csymbol>
              <ci id="p1.1.m1.1.9.1.1.cmml" xref="p1.1.m1.1.9.1.1">𝑡</ci>
              <cn type="integer" id="p1.1.m1.1.9.1.2.1.cmml" xref="p1.1.m1.1.9.1.2.1">2</cn>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.20.2.2.cmml" xref="p1.1.m1.1.20.2.2">
            <times id="p1.1.m1.1.20.2.2.1.cmml" xref="p1.1.m1.1.20.2.2.1"/>
            <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝐿</ci>
            <vector id="p1.1.m1.1.20.2.2.2.1.cmml" xref="p1.1.m1.1.20.2.2.2">
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑞</ci>
              <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
                <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">˙</ci>
                <ci id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">𝑞</ci>
              </apply>
              <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑡</ci>
            </vector>
            <apply id="p1.1.m1.1.20.2.2.3.cmml" xref="p1.1.m1.1.20.2.2.3">
              <csymbol cd="latexml" id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">differential-d</csymbol>
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑡</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle S\left[q\right]:=\int\limits_{{{t}_{1}}}^{{{t}_{2%
}}}{L\left(q,\dot{q},t\right)dt}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (1.835 KB / 497 B) :

S [ q ] := t 1 t 2 L ( q , q ˙ , t ) d t {\displaystyle S\left[q\right]:=\int \limits _{{t}_{1}}^{{t}_{2}}{L\left(q,{\dot {q}},t\right)dt}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle S\left[q\right]:=\int \limits _{{t}_{1}}^{{t}_{2}}{L\left(q,{\dot {q}},t\right)dt}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>S</mi>
        <mrow>
          <mo>[</mo>
          <mi>q</mi>
          <mo>]</mo>
        </mrow>
        <mo>:=</mo>
        <munderover>
          <mo>&#x222B;<!-- ∫ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>t</mi>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mn>1</mn>
              </mrow>
            </msub>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>t</mi>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mn>2</mn>
              </mrow>
            </msub>
          </mrow>
        </munderover>
        <mrow class="MJX-TeXAtom-ORD">
          <mi>L</mi>
          <mrow>
            <mo>(</mo>
            <mrow>
              <mi>q</mi>
              <mo>,</mo>
              <mrow class="MJX-TeXAtom-ORD">
                <mrow class="MJX-TeXAtom-ORD">
                  <mover>
                    <mi>q</mi>
                    <mo>&#x02D9;<!-- ˙ --></mo>
                  </mover>
                </mrow>
              </mrow>
              <mo>,</mo>
              <mi>t</mi>
            </mrow>
            <mo>)</mo>
          </mrow>
          <mi>d</mi>
          <mi>t</mi>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle S\left[q\right]:=\int \limits _{{t}_{1}}^{{t}_{2}}{L\left(q,{\dot {q}},t\right)dt}}</annotation>
  </semantics>
</math>

SVG (8.277 KB / 3.359 KB) :

{\displaystyle S\left[q\right]:=\int \limits _{{t}_{1}}^{{t}_{2}}{L\left(q,{\dot {q}},t\right)dt}}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Hamiltonsches Prinzip page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results