A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum

TL;DR

This paper introduces an explicit reversible symplectic integrator tailored for the symmetry-reduced, regularised planar 3-body problem with zero angular momentum, enabling accurate long-term simulations of complex orbital dynamics.

Contribution

It presents a novel symplectic integrator based on a globally regularised Hamiltonian decomposed into integrable polynomials, specifically designed for the symmetry-reduced 3-body problem.

Findings

Successfully applied to figure eight orbit, Pythagorean orbit, and collision orbit.

Demonstrates high accuracy and stability in numerical simulations.

Provides a new tool for studying complex three-body dynamics.

Abstract

We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This Hamiltonian is a sum of 10 polynomials each of which can be integrated exactly, and hence a symplectic integrator is constructed. The performance of the integrator is examined with three numerical examples: The figure eight, the pythagorean orbit, and a periodic collision orbit.