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

TL;DR

This paper investigates how Lagrangian orbits in the 3-body problem change as the space's curvature varies, revealing new orbit classes in curved geometries like elliptic and hyperbolic spaces.

Contribution

It introduces a comprehensive analysis of bifurcations of Lagrangian orbits across Euclidean, elliptic, and hyperbolic spaces, discovering new classes of orbits in curved geometries.

Findings

Existence of bifurcations of Lagrangian orbits with changing curvature

Discovery of new orbit families, including isosceles triangles in elliptic space

Extension of classical 3-body problem results to curved spaces

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.