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- W4382319547 abstract "The positive curved three body problem is a natural extension of the planar Newtonian three body problem to the sphere $mathbb{S}^2$. In this paper we study the extensions of the Euler and Lagrange Relative equilibria ($RE$ in short) on the plane to the sphere. The $RE$ on $mathbb{S}^2$ are not isolated in general. They usually have one-dimensional continuation in the three-dimensional shape space. We show that there are two types of bifurcations. One is the bifurcations between Lagrange $RE$ and Euler $RE$. Another one is between the different types of the shapes of Lagrange $RE$. We prove that bifurcations between equilateral and isosceles Lagrange $RE$ exist for equal masses case, and that bifurcations between isosceles and scalene Lagrange $RE$ exist for partial equal masses case." @default.
- W4382319547 created "2023-06-28" @default.
- W4382319547 creator A5071700946 @default.
- W4382319547 creator A5086354287 @default.
- W4382319547 date "2023-06-23" @default.
- W4382319547 modified "2023-09-25" @default.
- W4382319547 title "Continuations and bifurcations of relative equilibria for the positive curved three body problem" @default.
- W4382319547 doi "https://doi.org/10.48550/arxiv.2306.13838" @default.
- W4382319547 hasPublicationYear "2023" @default.
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