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Il Nuovo Cimento B (1971-1996)

, Volume 108, Issue 6, pp 657–667 | Cite as

On generalized Runge-Lenz vector and conserved symmetric tensor for central-potential systems with a monopole field on spaces of constant curvature

  • N. Katayama
Article
  • 51 Downloads

Summary

In classical mechanics, it was shown by Fradkin that there exist O(4) andSU(3) dynamical symmetries in a local sense for all central-potential problems in the three-dimensional Euclidean space. He constructed the generalized Runge-Lenz vector and the generalized conserved symmetric tensor for central-potential systems concretely. This article deals with central-potential systems with a monopole field on a space of constant curvature. An extension of Frandkin’s method together with the Boulware-Brown-Cahn-Ellis-Lee transformation is applied to obtain the generalized Runge-Lenz vector and the generalized conserved symmetric tensor for the present dynamical system. Global consideration is given to those conserved quantities for the Kepler motion and the harmonic oscillator. Further, the symmetry problem in the case of the Euclidean configuration space will be touched upon.

PACS

03.20 Classical mechanics of discrete systems: general mathematical aspects 

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Copyright information

© Società Italiana di Fisica 1993

Authors and Affiliations

  • N. Katayama
    • 1
  1. 1.Department of Systems and Control EngineeringOsaka Prefectural College of TechnologyOsakaJapan

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