DYNAMICS OF THE LEVITRON(TM)

The Levitron(TM) is an axisymmetric top magnetized parallel to its sym metry axis. It can levitate above a specially constructed magnetic bas e if spun rapidly enough (and, as we found, not too rapidly). We have written a complete, coupled, nondissipative Hamiltonian system that de scribes the dynamics of the top. The system is twelfth order and is to o complicated for general analysis. We have integrated the equations o f motion numerically and found a region of a two-dimensional manifold of initial conditions for which levitation persists. We find that the amplitude of the dynamic variables in the region of persistent levitat ion scales linearly with the initial tilt of the axis with respect to gravity. We have identified three distinct modes of failure that corre spond roughly to insufficient initial spin, too large an initial tilt and too great an initial spin. Our results are in general agreement wi th published observations and theoretical estimates.