English

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.

Keywords

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

R2 v1 2026-06-28T12:01:45.469Z