The Eight-Body Cubic Collision-Based Periodic Orbit
arXiv:2110.06174
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.
arXiv comment19 pages, 5 figures
References in corpus (3)
- Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem
- Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
- Symbolic Dynamics in the Elliptic Isosceles Restricted Three Body Problem