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

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 ${\mathbb{S}}^1$, but unstable if the bodies are considered in ${\mathbb{S}}^2$.

17 pages, 2 figures

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