Dynamics on the cone: closed orbits and superintegrability

Authors :: Brihaye, Y.
Kosiński, P.
Maślanka, P.
Publication Year :: 2013
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.<br />Comment: 15 pages, 3 figures; some references added, few misprints corrected