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Classical Kepler-Coulomb problem on SO(2, 2) hyperboloid |
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| Authors: | D Petrosyan G S Pogosyan |
| Institution: | 1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia 2. Physics Department, Yerevan State University, Yerevan, Armenia 3. Departamento de Matematicas, CUCEI, Universidad de Guadalajara, Jalisco, Mexico |
| Abstract: | In the present work, the problem of the motion of the classical particle in the Kepler-Coulomb field in three-dimensional hyperbolic space H 2 2 : z 2 0 + z 2 1 ? z 2 2 ? z 2 3 = R 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. |
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