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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/6639294 |
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| author | W. I. Skrypnik |
| author_facet | W. I. Skrypnik |
| author_sort | W. I. Skrypnik |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-49b2bd8f604f4c9aabf1a1c6486fc2ac |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-49b2bd8f604f4c9aabf1a1c6486fc2ac2025-08-20T02:39:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/66392946639294Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different DimensionsW. I. Skrypnik0Institute of Mathematics, Tereshchenkivska 3, Kyiv-4 01004, UkraineThe 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 |
| spellingShingle | W. I. Skrypnik Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions Advances in Mathematical Physics |
| title | 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_short | Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions |
| title_sort | equilibrium regular polygons and coulomb type dynamics in different dimensions |
| url | http://dx.doi.org/10.1155/2021/6639294 |
| work_keys_str_mv | AT wiskrypnik equilibriumregularpolygonsandcoulombtypedynamicsindifferentdimensions |