Dynamics of a Levitron under a periodic magnetic forcing

Abstract

The Levitron is a toy that consists of a spinning top that levitates over a magnetic base for a few minutes, until air drag decreases the spin rate below a certain limit. Stable levitation, lasting hours or even days, has been achieved for Levitrons that were externally driven by either an air jet or an alternating magnetic field. We report measurements of stable levitation for the latter case. We show that the top precession couples with the frequency of the alternating field, so that the precession period equals the period of the field. In addition, the top rotates around itself with the same period. We present numerical simulations that reproduce the essential features of this dynamics. It is also shown that the magnetic torque that drives the top is due to a misalignment between the magnetic dipole moment and the mechanical axis of the top.