Stability interchanges in a curved Sitnikov problem
Dynamical Systems
2017-01-27 v1 Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
We consider a curved Sitnikov problem, in which an infinitesimal particle moves on a circle under the gravitational influence of two equal masses in Keplerian motion within a plane perpendicular to that circle. There are two equilibrium points, whose stability we are studying. We show that one of the equilibrium points undergoes stability interchanges as the semi-major axis of the Keplerian ellipses approaches the diameter of that circle. To derive this result, we first formulate and prove a general theorem on stability interchanges, and then we apply it to our model. The motivation for our model resides with the -body problem in spaces of constant curvature.
Cite
@article{arxiv.1701.07451,
title = {Stability interchanges in a curved Sitnikov problem},
author = {Luis Franco-Pérez and Marian Gidea and Mark Levi and Ernesto Pérez-Chavela},
journal= {arXiv preprint arXiv:1701.07451},
year = {2017}
}