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Title: Classical Kepler-Coulomb problem on SO(2, 2) hyperboloid

In the present work, the problem of the motion of the classical particle in the Kepler-Coulomb field in three-dimensional hyperbolic space H{sub 2}{sup 2}: z{sub 2}{sup 0} + z{sub 2}{sup 1} - z{sub 2}{sup 2} - z{sub 2}{sup 3} = R{sup 2} is solved in the framework of Hamilton-Jacobi equation. The requirements for the existence of bounded motion of particle are formulated. The equation of the trajectory of particle is obtained, and it is shown that all the finite trajectories are closed. It is also demonstrated that under the certain values (zero or negative) of the separation constant A the fall of the particle onto the center takes place.
Authors:
;  [1]
  1. Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics (Russian Federation)
Publication Date:
OSTI Identifier:
22212644
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 76; Journal Issue: 10; Other Information: Copyright (c) 2013 Pleiades Publishing, Ltd.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COULOMB FIELD; HAMILTON-JACOBI EQUATIONS; HYDROGEN; PARTICLES; THREE-DIMENSIONAL CALCULATIONS; TRAJECTORIES