The Eight-Body Cubic Collision-Based Periodic Orbit
Dynamical Systems
2021-11-08 v2
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.
Cite
@article{arxiv.2110.06174,
title = {The Eight-Body Cubic Collision-Based Periodic Orbit},
author = {Skyler Simmons},
journal= {arXiv preprint arXiv:2110.06174},
year = {2021}
}
Comments
19 pages, 5 figures