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 S\'anchez-Cerritos; Shuqiang Zhu

arxiv: 1603.03339 · v2 · pith:WTKYYJU5new · submitted 2016-03-10 · 🧮 math.DS · math-ph· math.MP

Stability of fixed points and associated relative equilibria of the 3-body problem on mathbb S¹ and mathbb S²

Florin Diacu , Juan Manuel S\'anchez-Cerritos , Shuqiang Zhu This is my paper

classification 🧮 math.DS math-phmath.MP

keywords mathbbassociatedbodyequilibriafixedpointsproblemrelative

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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 $\mathbb S^2$.

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Stability of fixed points and associated relative equilibria of the 3-body problem on mathbb S¹ and mathbb S²

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