Stability of Levitrons

The Levitron is a magnetic spinning top which can levitate in the constant field of a repelling base magnet. The present work develops an exact theory of the Levitron with sit degrees of freedom. The stability of the symmetri c relative equilibrium is calculated. The main result is a complete classif ication of possible Levitrons that allow for an interval of stable spin rat es. Stability of the relative equilibrium is lost in Hamiltonian Hopf bifur cations if either the spin rate is too large or too small.