Balabanova, Nataliya and Montaldi, James (2021) Two body problem on a sphere in the presence of a uniform magnetic field. [MIMS Preprint]
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Abstract
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between the velocity and the radius of motion. For two identical particles, interacting via a cotangent potential, we show there are two families of relative equilibria, called Type I and Type II. The Type I relative equilibria exist for all strengths of the magnetic field, while those of Type II exist only if the field is sufficiently strong. The same is true if the particles are of equal mass but opposite charge. We also determine the stability of the two families of relative equilibria.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems |
| Depositing User: | Dr James Montaldi |
| Date Deposited: | 19 Jan 2021 09:59 |
| Last Modified: | 19 Jan 2021 09:59 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2799 |
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