Two-body problem on a sphere Reduction, stochasticity, periodic orbits
<|reference_start|>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.<|reference_end|>
@article{borisov2005two-body,
    title={Two-body problem on a sphere. Reduction, stochasticity, periodic orbits},
    author={A.V. Borisov, I.S. Mamaev, A.A. Kilin},
    journal={Regular and Chaotic Dynamics, 2004 Volume 9 Number 3},
    year={2005},
    archivePrefix={arXiv},
    eprint={nlin/0502027},
    primaryClass={nlin.CD cs.OH nlin.SI}
}