Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem

Abstract

We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces, and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of new classes of orbits. In particular, we find some families of isosceles triangles, which occur in elliptic space.

26 pages, 3 figures

References in corpus (4)

• Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2
• The classical N-body problem in the context of curved space
• Saari's Homographic Conjecture of the Three-Body Problem
• All the Lagrangian relative equilibria of the curved 3-body problem have equal masses

Cited by in corpus (3)

• Central configurations of the curved $N$-body problem
• Three dimensional central configurations in H3 and S3
• Attracting and repelling 2-body problems on a family of surfaces of constant curvature