Newton-Hooke type symmetry of anisotropic oscillators

TL;DR

This paper generalizes the Newton-Hooke type symmetry to anisotropic oscillators in the plane, showing it as the most general system with such symmetry and applying it to star escape phenomena.

Contribution

It extends the Newton-Hooke symmetry to anisotropic oscillators and demonstrates their maximal symmetry using the orbit method, with applications to astrophysical escape scenarios.

Findings

Generalization of Newton-Hooke symmetry to anisotropic oscillators

Anisotropic oscillators are the most general systems with this symmetry

Application to star escape from a galaxy

Abstract

The rotation-less Newton--Hooke - type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case. Star escape from a Galaxy is studied as application.