Two-body problem on a sphere in the presence of a uniform magnetic field

James Montaldi, Nataliya Balabanova

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)370-291
Number of pages22
JournalRegular and Chaotic Dynamics
Issue number4
Publication statusPublished - 9 Aug 2021


  • Relative equilibria
  • reduction
  • stability
  • bifurcations


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