The Octahedral Collision-Based Periodic Orbit in the Three-Dimensional Six-Body Problem

TL;DR

This paper constructs a symmetric periodic orbit with binary collisions in a 3D six-body problem, extending regularization techniques and analyzing its stability.

Contribution

It introduces a new highly-symmetric collision-based periodic orbit in three dimensions and extends regularization methods to analyze its properties.

Findings

Orbit exhibits binary collisions at the origin in a periodic pattern

The orbit is numerically constructed using initial conditions

The orbit is shown to be unstable

Abstract

We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes. Regularization of the collisions in the orbit is achieved by an extension of the Levi-Civita method. Initial conditions for the orbit are found numerically. In contrast to an earlier periodic collision-based orbit in three dimensions, this orbit is shown to be unstable.