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

2023/08/04 by Simmons, Skyler
#37J25 #37N05 #70F10 #70F16 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.11625

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.

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