Comment on `conservative discretizations of the Kepler motion'

TL;DR

This paper discusses the derivation of the exact integrator for Kepler motion, highlighting its connection to harmonic oscillator discretization and revisiting earlier related work.

Contribution

It presents a simple derivation of the exact Kepler integrator and emphasizes the relevance of previous discretizations of the harmonic oscillator in Kepler problems.

Findings

Exact integrator for Kepler motion can be derived from harmonic oscillator discretization.

The approach simplifies understanding of Kepler integrator derivation.

Previous work on harmonic oscillator discretization is relevant to Kepler problem.

Abstract

We show that the exact integrator for the classical Kepler motion, recently found by Kozlov ({\it J. Phys. A: Math. Theor.\} {\bf 40} (2007) 4529-4539), can be derived in a simple natural way (using well known exact discretization of the harmonic oscillator). We also turn attention on important earlier references, where the exact discretization of the 4-dimensional isotropic harmonic oscillator has been applied to the perturbed Kepler problem.