English

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 nn--body problem defined on surfaces of constant negative curvature. For the case of nn--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