Stability of Euler-Type Relative Equilibria in the Curved Three Body Problem

Abstract

We consider three point particles of masses m 1, m 2, m 3 moving on a two-dimensional surface of constant curvature k. It is well known that, locally, these surfaces are characterized by the sign of the curvature k. If k > 0, the surface is the two dimensional sphere S 2 of radius R = 1/k embedded in the Euclidian space.