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Display information for equation id:math.1991.6 on revision:1991
* Page found: Wirkungs- und Winkelvariable (eq math.1991.6)
(force rerendering)Occurrences on the following pages:
Hash: d9b3affd64618a2752325634ea4f3069
TeX (original user input):
\begin{align}
& {{p}_{\phi }}=\frac{\partial L}{\partial \dot{\phi }}=\frac{\partial T}{\partial \dot{\phi }}=m{{l}^{2}}\dot{\phi } \\
& H(\phi ,{{p}_{{\dot{\phi }}}})=T+V=\frac{{{p}_{\phi }}^{2}}{2m{{l}^{2}}}+mgl(1-\cos \phi ) \\
\end{align}TeX (checked):
{\begin{aligned}&{{p}_{\phi }}={\frac {\partial L}{\partial {\dot {\phi }}}}={\frac {\partial T}{\partial {\dot {\phi }}}}=m{{l}^{2}}{\dot {\phi }}\\&H(\phi ,{{p}_{\dot {\phi }}})=T+V={\frac {{{p}_{\phi }}^{2}}{2m{{l}^{2}}}}+mgl(1-\cos \phi )\\\end{aligned}}LaTeXML (experimental; uses MathML) rendering
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MathML (2.335 KB / 454 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><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mo>=</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="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>T</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo>=</mo><mi>m</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>H</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mi>T</mi><mo>+</mo><mi>V</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo>+</mo><mi>m</mi><mi>g</mi><mi>l</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>Translations to Computer Algebra Systems
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