The Octahedral Collision-Based Periodic Orbit in the Three-Dimensional Six-Body Problem
Dynamical Systems
2023-08-24 v1
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.
Cite
@article{arxiv.2308.11625,
title = {The Octahedral Collision-Based Periodic Orbit in the Three-Dimensional Six-Body Problem},
author = {Skyler Simmons},
journal= {arXiv preprint arXiv:2308.11625},
year = {2023}
}
Comments
26 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2110.06174