Stabilization of a movable magnet in the field of a stationary one by rotation

It is shown that a rotating body containing a permanent magnet may be in stable noncontact equilibrium when placed in the field of a stationary magnet. It is assumed that the magnets are of a cylindrical shape and their magnetizations are aligned with the cylinder axis. The field of the magnets is simulated by two turns with direct current, which makes it possible to analytically find the forces and force moments acting on the movable magnet subjected to the field of the stationary one. Instability of the equilibrium state of a suspended body when its weight is counterbalanced by the repulsive force exerted by a stationary magnet follows from the Earnshaw theorem. It is demonstrated here that such instability may be removed with gyroscopic forces due to rotation of the suspended body. It turns out that the rotation of the movable magnet may stabilize not only its unstable angular but also translational degrees of freedom, which is a newly discovered effect.