On the spinning motion of the hovering magnetic top

In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical t op. A classical top rotates about its own axis which precesses around a ver tical fixed external axis. The hovering magnetic top, on the other hand, ha s its axis slightly tilted and moves rigidly as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment , we see that a point at the rim of the top moves synchronously with the to p axis. We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We show that as a consequence, the minimum angular velocity required for stability is given by root mu H/(I-3 - I-1) for I-3 > I-1 and by root 4 mu HI1/I-3(2) for I-3 < I-1. Here, I-3 and I-1 are the principal and secondary moments of inertia , mu is the magnetic moment, and H is the magnetic field. For comparison, t he minimum angular velocity for a classical top is given by root 4 mu HI1/I -3(2) both for I-3 > I-1 and for I-3 < I-1. We also give experimental results that were taken with a top whose moment o f inertia II can be changed. These results show very good agreement with ou r calculations. (C) 1999 Elsevier Science B.V. All rights reserved.