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Hamiltonian from the equation of motion
The equation of motion is
$$(1+e\cos f)\frac{d^2\theta}{df^2}-2e\sin f\frac{d\theta}{df}-\frac{w^2}{2}\sin 2(f-\theta)=0,$$
where $0<e<1$, $w\in const$. Taking $q=\theta$ and $p=\frac{d\theta}{df}$, …
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Angular dependence of the element of mass of an ellipse
I have an ellipse (a ring, not a disk; its center of mass in $C$) with a constant linear density and mass $m$, with semi-axes $a>b$; $\alpha$ is a dynamical angle describing the orientation of the bod …