Y. Brihaye, P. Kosiński, P. Maślanka
Published 2013-10-11, updated 2013-10-24Version 2
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.
Comments: 15 pages, 3 figures; some references added, few misprints corrected
Superintegrability of the Fock-Darwin system
Superintegrability on sl(2)-coalgebra spaces
New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces
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