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

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  • W. I. Skrypnik

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.

Suggested Citation

  • W. I. Skrypnik, 2021. "Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-11, March.
    • Handle: RePEc:hin:jnlamp:6639294
    DOI: 10.1155/2021/6639294
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