Abstract
Separable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a \({\mathbb R}^2\) plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context.
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