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Title: Dynamics on the cone: Closed orbits and superintegrability

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 analysed for the case of Kepler and harmonic oscillator potentials. -- Highlights: •Bertrand’s theorem is generalized to the case of the motion on a cone. •The superintegrability of the dynamics on a cone is discussed. •The W-algebra of integrals of motion for Kepler and harmonic oscillator problems on a cone is derived.
Authors:
 [1] ;  [2] ;  [2]
  1. Department of Theoretical and Mathematical Physics, University of Mons, 20, Place du Parc, B7000 Mons (Belgium)
  2. Department of Theoretical Physics and Computer Science, University of Łódź, Pomorska 149/153, 90-236 Łódź (Poland)
Publication Date:
OSTI Identifier:
22314812
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 344; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CONES; HARMONIC OSCILLATORS; INTEGRALS; MATHEMATICAL MODELS; ORBITS; POTENTIALS; SURFACES