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Display information for equation id:math.1989.33 on revision:1989
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1989.33)
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Hash: 9e37a5eb3b6a260bfc585558f3e44395
TeX (original user input):
p=\left( \frac{\partial S(q,P,t)}{\partial q} \right)=\frac{dW}{dq}=m\omega \sqrt{\frac{2\alpha }{m{{\omega }^{2}}}-{{q}^{2}}}=\sqrt{2\alpha m}\cos \left( \omega (t+\beta ) \right)
TeX (checked):
p=\left({\frac {\partial S(q,P,t)}{\partial q}}\right)={\frac {dW}{dq}}=m\omega {\sqrt {{\frac {2\alpha }{m{{\omega }^{2}}}}-{{q}^{2}}}}={\sqrt {2\alpha m}}\cos \left(\omega (t+\beta )\right)
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MathML (1.776 KB / 395 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>p</mi><mo>=</mo><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>S</mi><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</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>=</mo><mi>m</mi><mi>ω</mi><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><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>−</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>α</mi><mi>m</mi></mrow></msqrt></mrow><mi>cos</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ω</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>β</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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