Stability of fixed points and associated relative equilibria of the $3$-body problem on $\mathbb S^1$ and $\mathbb S^2$
Dynamical Systems
2017-01-06 v2 Mathematical Physics
math.MP
Abstract
We prove that the fixed points of the curved 3-body problem and their associated relative equilibria are Lyapunov stable if the solutions are restricted to , but unstable if the bodies are considered in .
Cite
@article{arxiv.1603.03339,
title = {Stability of fixed points and associated relative equilibria of the $3$-body problem on $\mathbb S^1$ and $\mathbb S^2$},
author = {Florin Diacu and Juan Manuel Sánchez-Cerritos and Shuqiang Zhu},
journal= {arXiv preprint arXiv:1603.03339},
year = {2017}
}
Comments
17 pages, 2 figures