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Display information for equation id:math.1994.6 on revision:1994
* Page found: Wirkungs- und Winkelvariable (eq math.1994.6)
(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}}
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MathML (2.093 KB / 430 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mo stretchy="false">=</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><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mfrac></mrow><mo stretchy="false">=</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><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mi>m</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mover><mi>ϕ</mi><mo>˙</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>H</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>T</mi><mo stretchy="false">+</mo><mi>V</mi><mo stretchy="false">=</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 stretchy="false">+</mo><mi>m</mi><mi>g</mi><mi>l</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">−</mo><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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