Stability of Levitron$^{\textrm{TM}}$ revisited

This note discusses some issues related to stability of stationary motion of hovering magnetized top in a homogeneous magnetic field. Stability of synchronous motion is analyzed using the simplified model in which the hovering motion of the center of mass is ignored. Stability boundaries are derived using Lyapunov direct method. In particular, it is shown that, for a given angle $\Delta$ between magnetic moment dipole and principal axis of the top, there is an interval of stationary values of nutation angle $\theta_0$ for which the stationary synchronous motion is stable.