Two-body problem on a sphere. Reduction, stochasticity, periodic orbits

Details Two-body problem on a sphere. Reduction, stochasticity, periodic orbits Two-body problem on a sphere. Reduction, stochasticity, periodic orbits

2005-02-11

arxiv.org/abs/nlin/0502027v1

Regular and Chaotic Dynamics, 2004 Volume 9 Number 3

Nonlinear Sciences

Chaotic Dynamics

15 pages, 6 figures

Scientific paper

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.

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