Relative Equilibria in curved restricted 4-body problems
Classical Analysis and ODEs
2019-08-15 v1
Abstract
We consider the curved 4-body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configu- rations on the equator of the sphere, we study two restricted 4-body problems, one in which two masses are negligible, and another in which only one mass is negligible. In the former we prove the evidence square-like relative equilibria, whereas in the latter we discuss the existence of kite-shaped relative equilibria.
Cite
@article{arxiv.1801.02126,
title = {Relative Equilibria in curved restricted 4-body problems},
author = {Florin Diacu and Sawsan Alhowaity},
journal= {arXiv preprint arXiv:1801.02126},
year = {2019}
}