Zur Navigation springen
Zur Suche springen
General
Display information for equation id:math.1411.128 on revision:1411
* Page found: Symmetrien und Erhaltungsgrößen (eq math.1411.128)
(force rerendering)Occurrences on the following pages:
Hash: 8a6ce2eb50564b82992123bd96b5a40f
TeX (original user input):
\begin{align}
& I=\frac{\partial \bar{L}}{\partial {{{\dot{q}}}_{f+1}}}=\frac{\partial \bar{L}}{\partial \left( \frac{dt}{d\tau } \right)}=L+\sum\limits_{k=1}^{f}{\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}\left( -\frac{1}{{{\left( \frac{dt}{d\tau } \right)}^{2}}} \right)\frac{d{{q}_{k}}}{d\tau }\frac{dt}{d\tau }} \\
& =L-\sum\limits_{k=1}^{f}{\left( \frac{\partial L}{\partial \left( {{{\dot{q}}}_{k}} \right)} \right){{{\dot{q}}}_{k}}}=T-V-2T=-(T-V) \\
\end{align}
TeX (checked):
{\begin{aligned}&I={\frac {\partial {\bar {L}}}{\partial {{\dot {q}}_{f+1}}}}={\frac {\partial {\bar {L}}}{\partial \left({\frac {dt}{d\tau }}\right)}}=L+\sum \limits _{k=1}^{f}{{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}\left(-{\frac {1}{{\left({\frac {dt}{d\tau }}\right)}^{2}}}\right){\frac {d{{q}_{k}}}{d\tau }}{\frac {dt}{d\tau }}}\\&=L-\sum \limits _{k=1}^{f}{\left({\frac {\partial L}{\partial \left({{\dot {q}}_{k}}\right)}}\right){{\dot {q}}_{k}}}=T-V-2T=-(T-V)\\\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 (4.911 KB / 588 B) :
<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></mtd><mtd><mi>I</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>f</mi><mo>+</mo><mn>1</mn></mrow></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>τ</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo>=</mo><mi>L</mi><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>τ</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>τ</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>τ</mi></mrow></mrow></mfrac></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>L</mi><mo>−</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>L</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow><mo>=</mo><mi>T</mi><mo>−</mo><mi>V</mi><mo>−</mo><mn>2</mn><mi>T</mi><mo>=</mo><mo>−</mo><mo stretchy="false">(</mo><mi>T</mi><mo>−</mo><mi>V</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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 Symmetrien und Erhaltungsgrößen page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results