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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |