On the non-existence of hyperbolic polygonal relative equilibria for the negative curved $n$--body problem with equal masses
Dynamical Systems
2016-12-30 v1
Abstract
We consider the --body problem defined on surfaces of constant negative curvature. For the case of --equal masses we prove that the hyperbolic relative equilibria with a regular polygonal shape do not exist. In particular the Lagrangian (three equal distances) hyperbolic relative equilibria do not exist. We also show the existence of a new class of hyperbolic collinear relative equilibria for the five body problem on surfaces of constant negative curvature.
Keywords
Cite
@article{arxiv.1612.09270,
title = {On the non-existence of hyperbolic polygonal relative equilibria for the negative curved $n$--body problem with equal masses},
author = {Ernesto Perez-Chavela and Juan Manuel Sanchez-Cerritos},
journal= {arXiv preprint arXiv:1612.09270},
year = {2016}
}
Comments
11 pages, 1 figure