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

W. I. Skrypnik

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: The equation of motion in ℝd of n generalized point charges interacting via the s‐dimensional Coulomb potential, which contains for d = 2 a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative n − 1 > 2 charges and their masses are equal or n = 3 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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https://doi.org/10.1155/2021/6639294

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6639294

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