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

Journal Article · Tue Oct 15 00:00:00 EDT 2013 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778813090135· OSTI ID:22212644

Petrosyan, D., E-mail: [e-mail]; Pogosyan, G. S., E-mail: [e-mail] ^[1]

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1. Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics (Russian Federation)

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.

• OSTI ID: 22212644
• Journal Information: Physics of Atomic Nuclei, Vol. 76, Issue 10; Other Information: Copyright (c) 2013 Pleiades Publishing, Ltd.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COULOMB FIELD
HAMILTON-JACOBI EQUATIONS
HYDROGEN
PARTICLES
THREE-DIMENSIONAL CALCULATIONS
TRAJECTORIES