All the Lagrangian relative equilibria of the curved 3-body problem have equal masses

Florin Diacu; Sergiu Popa

doi:10.1063/1.4900833

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arXiv · 1409.5073

All the Lagrangian relative equilibria of the curved 3-body problem have equal masses

Florin Diacu·Sergiu Popa

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Abstract

We consider the 3-body problem in 3-dimensional spaces of nonzero constant Gaussian curvature and study the relationship between the masses of the Lagrangian relative equilibria, which are orbits that form a rigidly rotating equilateral triangle at all times. There are three classes of Lagrangian relative equilibria in 3-dimensional spaces of constant nonzero curvature: positive elliptic and positive elliptic-elliptic, on 3-spheres, and negative elliptic, on hyperbolic 3-spheres. We prove that all these Lagrangian relative equilibria exist only for equal values of the masses.

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Florin Diacu, Sergiu Popa. 2014-09-17. All the Lagrangian relative equilibria of the curved 3-body problem have equal masses. https://doi.org/10.1063/1.4900833

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