– PhysikWiki

General

Display information for equation id:math.870.13 on revision:870

* Page found: Hamiltonsches Prinzip (eq math.870.13)

Occurrences on the following pages:

Hamiltonsches Prinzip Eq: math.870.13

Hash: 70f301ff1b2356b0e8ea9ec5670fc4f3

TeX (original user input):

\begin{align}
   \delta S\left[ q \right] & =- \cancel {\left[ {{\partial }_{{\dot{q}}}}L\delta q \right]_{{{t}_{1}}}^{{{t}_{2}}}} -\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{\partial }_{q}}L\delta q-{{d}_{t}}\left( {{\partial }_{{\dot{q}}}}L \right)\delta q \right)dt} \\ 
 & =\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L\delta qdt}  
\end{align}

TeX (checked):

{\begin{aligned}\delta S\left[q\right]&=-{\cancel {\left[{{\partial }_{\dot {q}}}L\delta q\right]_{{t}_{1}}^{{t}_{2}}}}-\int \limits _{{t}_{1}}^{{t}_{2}}{\left({{\partial }_{q}}L\delta q-{{d}_{t}}\left({{\partial }_{\dot {q}}}L\right)\delta q\right)dt}\\&=\int \limits _{{t}_{1}}^{{t}_{2}}{\left({{d}_{t}}{{\partial }_{\dot {q}}}-{{\partial }_{q}}\right)L\delta qdt}\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (3.044 KB / 524 B) :

\begin{aligned} δ S [q] & = - {[\partial_{\dot{q}} L δ q]}_{t_{1}}^{t_{2}} - \int_{t_{1}}^{t_{2}} (\partial_{q} L δ q - d_{t} (\partial_{\dot{q}} L) δ q) d t \\ = \int_{t_{1}}^{t_{2}} (d_{t} \partial_{\dot{q}} - \partial_{q}) L δ q d t \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mi>&#x03B4;</mi><mi>S</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd><mtd><mo>=</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><menclose notation="updiagonalstrike"><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mi>L</mi><mi>&#x03B4;</mi><mi>q</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msubsup></menclose></mrow><mo>&#x2212;</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mi>L</mi><mi>&#x03B4;</mi><mi>q</mi><mo>&#x2212;</mo><msub><mi>d</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mi>L</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>&#x03B4;</mi><mi>q</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>t</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>d</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><msub><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mo>&#x2212;</mo><msub><mi>&#x2202;</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>L</mi><mi>&#x03B4;</mi><mi>q</mi><mi>d</mi><mi>t</mi></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$δ$

$S$

$q$

$\dot{q}$

$L$

$δ$

$q$

$t_{1}$

$t_{2}$

$t_{1}$

$t_{2}$

$q$

$L$

$δ$

$q$

$d_{t}$

$\dot{q}$

$L$

$δ$

$q$

$t$

$t_{1}$

$t_{2}$

$d_{t}$

$\dot{q}$

$q$

$L$

$δ$

$q$

$t$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche