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Display information for equation id:math.1989.35 on revision:1989
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1989.35)
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Hash: 8f6429f6a751ce1b0be964c4d3064043
TeX (original user input):
\begin{align}
& \Rightarrow {{q}_{0}}=\frac{1}{\omega }\sqrt{\frac{2\alpha }{m}}\sin \left( \omega (\beta ) \right) \\
& 0={{p}_{0}}=\sqrt{2\alpha m}\cos \left( \omega (\beta ) \right) \\
& \Rightarrow \beta =\frac{\pi }{2\omega }\Rightarrow {{q}_{0}}=\sqrt{\frac{2\alpha }{m{{\omega }^{2}}}} \\
& \Rightarrow \alpha =\frac{m}{2}{{\omega }^{2}}{{q}_{0}}^{2}=E \\
\end{align}
TeX (checked):
{\begin{aligned}&\Rightarrow {{q}_{0}}={\frac {1}{\omega }}{\sqrt {\frac {2\alpha }{m}}}\sin \left(\omega (\beta )\right)\\&0={{p}_{0}}={\sqrt {2\alpha m}}\cos \left(\omega (\beta )\right)\\&\Rightarrow \beta ={\frac {\pi }{2\omega }}\Rightarrow {{q}_{0}}={\sqrt {\frac {2\alpha }{m{{\omega }^{2}}}}}\\&\Rightarrow \alpha ={\frac {m}{2}}{{\omega }^{2}}{{q}_{0}}^{2}=E\\\end{aligned}}
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