Stability of fixed points and associated relative equilibria of the   $3$-body problem on $\mathbb S^1$ and $\mathbb S^2$
  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 $\mathbb S^2$. 
Florin Diacu, Juan Manuel S\'anchez-Cerritos, and Shuqiang Zhu
math.DS math-ph math.MP