Families of classical subgroup separable superintegrable systems

TL;DR

This paper introduces a method to find complete integrals for classical Hamiltonians that separate in subgroup coordinates, demonstrating superintegrability in various generalized oscillator and Kepler-Coulomb systems, including on non-conformally flat spaces.

Contribution

It presents a new method for determining integrals in subgroup coordinates, extending superintegrability results to broader classes of systems and spaces.

Findings

Successfully determines integrals for generalized oscillator systems

Demonstrates superintegrability of Kepler-Coulomb systems

Provides an example on a non-conformally flat space

Abstract

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.