Transform the input cartesian position and velocity to action-angle coordinates in the Isochrone potential. See Section 3.5.2 in Binney & Tremaine (2008), and be aware of the errata entry for Eq. 3.225.
This transformation is analytic and can be used as a “toy potential” in the Sanders & Binney (2014) formalism for computing action-angle coordinates in any potential.
This function is included as a method of the
IsochronePotentialand it is recommended to call