Hyperbolic Shirts fit a 4-body Problem
Dynamical Systems
2016-11-10 v2 Differential Geometry
Abstract
Consider the equal mass planar -body problem with a potential corresponding to an inverse \textit{cube} force. The Jacobi-Maupertuis principle reparametrizes the dynamics as geodesics of a certain metric. We examine the curvature of this geodesic flow in the reduced space on the collinear and parallelogram invariant surfaces and derive some dynamical consequences. This proves a numerical conjecture of [4].
Cite
@article{arxiv.1610.08165,
title = {Hyperbolic Shirts fit a 4-body Problem},
author = {Connor Jackman and Josué Meléndez},
journal= {arXiv preprint arXiv:1610.08165},
year = {2016}
}
Comments
14 pages, 8 figures