The Eight-Body Cubic Collision-Based Periodic Orbit

TL;DR

This paper constructs and analyzes a highly symmetric eight-body periodic orbit in three dimensions, demonstrating collision regularization, numerical initial conditions, and stability properties.

Contribution

It introduces a new symmetric eight-body orbit with collision regularization and provides stability analysis, including evidence for higher-order stability.

Findings

Constructed a symmetric eight-body periodic orbit in 3D.

Regularized collisions using an extended Levi-Civita method.

Numerical evidence suggests potential higher-order stability.

Abstract

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. 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. Linear stability of the orbit is then shown using a technique by Roberts. Evidence toward higher-order stability is presented as an additional result of a numerical calculation.