Two-body problem on a sphere. Reduction, stochasticity, periodic orbits
  We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a system with two degrees of freedom and give a number of remarkable periodic orbits. We also discuss integrability and stochastization of the motion. 
A.V. Borisov, I.S. Mamaev, A.A. Kilin