Periodic solutions for the Lorentz force equation with singular potentials

TL;DR

This paper establishes conditions under which periodic solutions exist for the Lorentz force equation, especially in models with singular potentials such as Coulomb or magnetic dipole fields.

Contribution

It provides new sufficient conditions for periodic solutions in Lorentz force models with singular electromagnetic potentials.

Findings

Existence of periodic solutions under specific conditions.

Applicability to Coulomb-like and magnetic dipole potentials.

Extension of previous results to singular potential cases.

Abstract

We provide sufficient conditions for the existence of periodic solutions of the of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant models with singularities like Coulomb-like electric potentials or the magnetic dipole.