Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions

W. I. Skrypnik

Advances in Mathematical Physics, 2021, vol. 2021, 1-11

Abstract:

The equation of motion in of generalized point charges interacting via the - dimensional Coulomb potential, which contains for a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative charges and their masses are equal or and the charges are different. They describe a motion of negative charges along identical orbits around the positive immobile charge at the origin in such a way that their coordinates coincide with vertices of regular polygons centered at the origin. Bounded solutions converging to an equilibrium in the infinite time for the considered equation without a magnetic field are also obtained. A condition permitting the existence of such solutions is proposed.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:6639294

DOI: 10.1155/2021/6639294

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