Stable orbital motion of magnetic dipole in the field of permanent magnets

In this paper we aim to give a constructive proof of the existence of stable orbital motions of the bodies in the systems which interact only via magnetic forces. To demonstrate this, we give an example of a magnetic system for which we analytically prove Gμ-stability. We study the dynamics of a small magnetic body, a magnetic dipole, that performs the quasi-orbital motion in the field of two fixed magnetic poles of opposite signs placed at the system’s axis. We use the generalized energy–momentum method to find the conditions of stability of relative equilibria. We also give the realizable physical parameters of the system. •Constructive proof of the stable orbits in magnetic systems is given analytically.•Generalized energy–momentum method is applied in order to prove the Gμ stability.•Example of physical parameters that satisfy the stability conditions is given.