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

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

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...

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Main Author: W. I. Skrypnik
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/6639294
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spelling doaj-49b2bd8f604f4c9aabf1a1c6486fc2ac2021-07-02T18:36:25ZengHindawi LimitedAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/6639294Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different DimensionsW. I. Skrypnik0Institute of MathematicsThe 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.http://dx.doi.org/10.1155/2021/6639294
collection DOAJ
language English
format Article
sources DOAJ
author W. I. Skrypnik
spellingShingle W. I. Skrypnik
Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
Advances in Mathematical Physics
author_facet W. I. Skrypnik
author_sort W. I. Skrypnik
title Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
title_short Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
title_full Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
title_fullStr Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
title_full_unstemmed Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions
title_sort equilibrium, regular polygons, and coulomb-type dynamics in different dimensions
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9139
publishDate 2021-01-01
description 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.
url http://dx.doi.org/10.1155/2021/6639294
work_keys_str_mv AT wiskrypnik equilibriumregularpolygonsandcoulombtypedynamicsindifferentdimensions
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