Particle dynamics in a magnetic field: symplectic reduction and classification of singular trajectories

Abstract

Abstract The paper studies the dynamics of a classical non-relativistic charged particle moving in a superposition of force-free and constant magnetic fields. Using the first integrals of the problem, a symplectic reduction of the corresponding Newton-Lorentz equations to an auxiliary two-dimensional Hamiltonian system is performed. By the linearisation method, the types of singular points of the reduced Hamiltonian system are classified. The results obtained are applied to the problem of studying the trajectories of the original Hamiltonian system that are close to singular trajectories.