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Display information for equation id:math.1982.29 on revision:1982
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1982.29)
(force rerendering)Occurrences on the following pages:
Hash: 340501f09f5e72c36a5ebf55c6eb3c48
TeX (original user input):
\begin{align}
& {{\left( \frac{dW}{dq} \right)}^{2}}={{m}^{2}}{{\omega }^{2}}\left( \frac{2\alpha }{m{{\omega }^{2}}}-{{q}^{2}} \right) \\
& W=m\omega \int{dq}\sqrt{\left( \frac{2\alpha }{m{{\omega }^{2}}}-{{q}^{2}} \right)} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\left({\frac {dW}{dq}}\right)}^{2}}={{m}^{2}}{{\omega }^{2}}\left({\frac {2\alpha }{m{{\omega }^{2}}}}-{{q}^{2}}\right)\\&W=m\omega \int {dq}{\sqrt {\left({\frac {2\alpha }{m{{\omega }^{2}}}}-{{q}^{2}}\right)}}\\\end{aligned}}
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MathML (2.218 KB / 395 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"><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>W</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></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"><mn>2</mn><mi>α</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">−</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>W</mi><mo stretchy="false">=</mo><mi>m</mi><mi>ω</mi><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>q</mi></mrow><mrow data-mjx-texclass="ORD"><msqrt><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"><mn>2</mn><mi>α</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">−</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></msqrt></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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