About the Keplerization of motion in any central force field

TL;DR

This paper reviews and extends the keplerization method for one-body motion in central force fields, providing a homogenization approach that reveals dynamical symmetry groups and their global extensions.

Contribution

It reformulates keplerization into a general homogenization method applicable to all bounded motions in central force fields, and demonstrates how to identify and extend dynamical symmetry groups.

Findings

Provides a unified homogenization framework for keplerization

Proves the existence of dynamical symmetry groups in these systems

Shows how to extend local symmetry groups to global ones

Abstract

The method of keplerization of one-body motion in any central force field, introduced by Martinusi and Gurfil in 2012, is reviewed and reformulated into a general homogenization method which applies to any kind of bounded motion. It is also shown how this extended method provides a proof of the existence of a dynamical symmetry group and how it can be used to extend that group to a global symmetry group, for any such system