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Spherical isochrone model

{title2=$J_r$}

For specific energy $E<0$ and specific angular momentum $L$,
$$
J_r=\frac{GM}{\sqrt{-2E}}
-\frac12\left(L+\sqrt{L^2+4GMb}\right).
$$
Consequently the Hamiltonian in actions is
$$
H(J_r,L)=-\frac{2(GM)^2}
{\left(2J_r+L+\sqrt{L^2+4GMb}\right)^2}.
$$

Radial action of the spherical isochrone model

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 320 / 2 / d / Solution

Radial action of the spherical isochrone model ( $J_{r}$ )

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Radial action of the spherical isochrone model (Jr​)

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