Hyperbolic Shirts fit a 4-body Problem

2016/10/26 by Jackman, Connor, Meléndez, Josué
#37N05 #70F10 #70G45 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.08165

Abstract

Consider the equal mass planar 4-body problem with a potential corresponding to an inverse 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].

Related

• Constructing the Hyperbolic Plane as the reduction of a three-body\n problem
• No hyperbolic pants for the 4-body problem
• Fitting Hyperbolic Pants to a Three-Body Problem
• A N-body problem with weak force potential through Hamilton-Jacobi equation approach
• Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem