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.
Citation:
Borisov A. V., Mamaev I. S., Kilin A. A., Two-body problem on a sphere. Reduction, stochasticity, periodic orbits, Regular and Chaotic Dynamics,
2004, Volume 9, Number 3,
pp. 265-279