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Display information for equation id:math.1990.34 on revision:1990
* Page found: Wirkungs- und Winkelvariable (eq math.1990.34)
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Hash: 0f78b956640a1a8a9e0ff2a154ae0abe
TeX (original user input):
\begin{align}
& I(E)=\oint{pdq}=2m\omega \int\limits_{{{q}_{-}}}^{{{q}_{+}}}{{}}\sqrt{\frac{2E}{m{{\omega }^{2}}}-{{q}^{2}}}dq \\
& I(E)=2m\omega \left[ \frac{q}{2}\sqrt{\frac{2E}{m{{\omega }^{2}}}-{{q}^{2}}}+\frac{E}{m{{\omega }^{2}}}\arcsin \frac{q}{\sqrt{\frac{2E}{m{{\omega }^{2}}}}} \right]_{q+}^{q-}=\frac{2\pi }{\omega }E \\
\end{align}
TeX (checked):
{\begin{aligned}&I(E)=\oint {pdq}=2m\omega \int \limits _{{q}_{-}}^{{q}_{+}}{}{\sqrt {{\frac {2E}{m{{\omega }^{2}}}}-{{q}^{2}}}}dq\\&I(E)=2m\omega \left[{\frac {q}{2}}{\sqrt {{\frac {2E}{m{{\omega }^{2}}}}-{{q}^{2}}}}+{\frac {E}{m{{\omega }^{2}}}}\arcsin {\frac {q}{\sqrt {\frac {2E}{m{{\omega }^{2}}}}}}\right]_{q+}^{q-}={\frac {2\pi }{\omega }}E\\\end{aligned}}
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MathML (3.655 KB / 566 B) :
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