Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions. (29th March 2021)

• Record Type: Journal Article
• Authors: Skrypnik, W. I.
• Other Names: Giorgio Ivan Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2021(2021)
• Publication Date: 2021-03-29
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2021/6639294
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : The equation of motion in ℝ d 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.