Stability of Levitrons

The Levitron is a magnetic spinning top which can levitate in the constant field of a repelling base magnet. An explanation for the stability of the L evitron using an adiabatic approximation has been given by Berry. In experi ments the top eventually loses stability at a critical spin rate which cann ot be predicted by Berry's approach. The present work develops an exact the ory of the Levitron with six degrees of freedom which allows for the calcul ation of critical spin rates. The main result is a complete classification of possible Levitrons that allow for an interval of stable spin rates. Stab ility of the relative equilibrium is lost in Hamiltonian Hopf bifurcations if either the spin rate is too large or too small. (C) 1999 Published by El sevier Science B.V. All rights reserved.