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arXiv · 1001.1789

Homographic solutions of the curved 3-body problem

Florin Diacu·Ernesto Perez-Chavela
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Abstract

In the 2-dimensional curved 3-body problem, we prove the existence of Lagrangian and Eulerian homographic orbits, and provide their complete classification in the case of equal masses. We also show that the only non-homothetic hyperbolic Eulerian solutions are the hyperbolic Eulerian relative equilibria, a result that proves their instability.

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Florin Diacu, Ernesto Perez-Chavela. 2010-01-26. Homographic solutions of the curved 3-body problem. https://arxiv.org/abs/1001.1789

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