Three-body relative equilibria on $\mathbb{S}^2$ I: Euler configurations

Toshiaki Fujiwara; Ernesto Perez-Chavela

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arXiv · 2202.10351

Three-body relative equilibria on $\mathbb{S}^2$ I: Euler configurations

Toshiaki Fujiwara·Ernesto Perez-Chavela

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Abstract

Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential depending only on the mutual distances among the bodies. With the above techniques we do an analysis of the relative equilibria for the case of three bodies when they are moving on the same geodesic (Euler configurations).

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Toshiaki Fujiwara, Ernesto Perez-Chavela. 2022-02-21. Three-body relative equilibria on $\mathbb{S}^2$ I: Euler configurations. https://arxiv.org/abs/2202.10351

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