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Display information for equation id:math.1990.7 on revision:1990
* Page found: Wirkungs- und Winkelvariable (eq math.1990.7)
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Hash: 8fdf289f28156aae1db0823b9bedb25d
TeX (original user input):
\begin{align}
& \dot{\phi }=\frac{\partial H(\phi ,{{p}_{{\dot{\phi }}}})}{\partial {{p}_{\phi }}}=\frac{{{p}_{\phi }}}{m{{l}^{2}}} \\
& {{{\dot{p}}}_{\phi }}=-\frac{\partial H(\phi ,{{p}_{{\dot{\phi }}}})}{\partial \phi }=-mgl\sin \phi \\
\end{align}
TeX (checked):
{\begin{aligned}&{\dot {\phi }}={\frac {\partial H(\phi ,{{p}_{\dot {\phi }}})}{\partial {{p}_{\phi }}}}={\frac {{p}_{\phi }}{m{{l}^{2}}}}\\&{{\dot {p}}_{\phi }}=-{\frac {\partial H(\phi ,{{p}_{\dot {\phi }}})}{\partial \phi }}=-mgl\sin \phi \\\end{aligned}}
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MathML (2.005 KB / 412 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"><mover><mi>ϕ</mi><mo>˙</mo></mover><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><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></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>p</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><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></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϕ</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>m</mi><mi>g</mi><mi>l</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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