Dynamics on the cone: closed orbits and superintegrability
arXiv:1310.3081 · doi:10.1016/j.aop.2014.02.022
Abstract
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of Kepler and harmonic oscillator potentials.
15 pages, 3 figures; some references added, few misprints corrected