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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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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)

LaTeXML (experimentell; verwendet MathML) rendering

MathML (14.101 KB / 2.044 KB) :

p = ( ∂ ⁡ S ⁢ ( q , P , t ) ∂ ⁡ q ) = d ⁢ W d ⁢ q = m ⁢ ω ⁢ 2 ⁢ α m ⁢ ω 2 - q 2 = 2 ⁢ α ⁢ m ⁢ cos ⁡ ( ω ⁢ ( t + β ) ) 𝑝 𝑆 𝑞 𝑃 𝑡 𝑞 𝑑 𝑊 𝑑 𝑞 𝑚 𝜔 2 𝛼 𝑚 superscript 𝜔 2 superscript 𝑞 2 2 𝛼 𝑚 𝜔 𝑡 𝛽 {\displaystyle{\displaystyle 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 (experimentell; keine Bilder) rendering

MathML (1.776 KB / 395 B) :

p=(∂S(q,P,t)∂q)=dWdq=mω2αmω2−q2=2αmcos⁡(ω(t+β))

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