Stability of fixed points and associated relative equilibria of the $3$-body problem on ${\mathbb{S}}^1$ and ${\mathbb{S}}^2$

Florin Diacu, Juan Manuel Sánchez-Cerritos, Shuqiang Zhu

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 ${\mathbb{S}}^1$, but unsta…