d'Alembert-type scheme with a chain regularization for N-body problem

TL;DR

This paper introduces a novel orbital integration scheme for the N-body problem that preserves most conserved quantities and accurately reproduces periodic orbits, extending previous methods with a chain regularization approach.

Contribution

It develops a d'Alembert-type scheme with chain regularization for N-body problems, capable of preserving conserved quantities and accurately capturing periodic orbits.

Findings

Preserves all conserved quantities except angular momentum.

Accurately reproduces some periodic orbits.

Extends previous three-body problem schemes to general N-body systems.

Abstract

We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an extension of a d'Alembert-type scheme (Betsch 2005) for constrained Hamiltonian systems. It also coincides with the discrete-time general three-body problem (Minesaki 2013) for particle number N = 3. Although the proposed scheme is only second-order accurate, it can accurately reproduce some periodic orbits, which generic geometric numerical integrators cannot do.