The Optimal Reduction of a 2-Body Problem in R^3

TL;DR

This paper develops an optimal reduction method for a two-body Hamiltonian system in three-dimensional space, providing explicit parametrizations and comparing it with standard reduction techniques, with applications in astronomy.

Contribution

It introduces explicit parametrizations for optimal reduction of a two-body problem in R^3 and compares it with Marsden-Weinstein reduction, addressing geometric and dynamical complexities.

Findings

Explicit parametrizations for the reduction process

Comparison between optimal and Marsden-Weinstein reduction

Potential applications to binary systems in astronomy

Abstract

In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit expressions in order to deal with geometric and dynamical aspects of the reduction process. For this system, the standard assumptions of the Marsden-Weinstein reduction process are only partially satisfied while optimal reduction can be readily applied, and we study a comparison between those two reduction processes. We describe potential applications to the study of Post-Newtonian Hamiltonian systems for binary systems in astronomy.