On generalized Runge-Lenz vector and conserved symmetric tensor for central-potential systems with a monopole field on spaces of constant curvature
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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.
PACS03.20 Classical mechanics of discrete systems: general mathematical aspects
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