  The stability of the orbital motion of two long cylindrical magnets
interacting exclusively with magnetic forces is described. To carry out
analytical studies a model of magnetically interacting symmetric tops [1] is
used. The model was previously developed within the quasi-stationary approach
for an electromagnetic field based on the general expression of the energy of
interacting magnetic bodies [2]. A special role in the investigation of the
stability of orbital motions is played by the so-called relative equilibria
[3], i.e. the trajectories of the system dynamics which are at the same time
one-parameter subgroups of the system invariance group. Nowadays their
stability is normally investigated using two similar approaches --
energy-momentum and energy-Casimir methods. The most suitable criterion for the
system stability investigation was formulated in the theorem of [4]; this
stability criterion successfully generalizes both the methods mentioned above
and covers the Hamiltonian formalism based on Poisson structures [1]. The
necessary and sufficient conditions for the circular orbit stability are
derived from this theorem.
