On the dynamical stability of the hovering magnetic top

In this paper we analyze the dynamic stability of the hovering magnetic top from first principles without using any preliminary assumptions. We write down the equations of motion for all six degrees of freedom and solve them analytically around the equilibrium solution. Using this solution we then f ind conditions which the height of the hovering top above the base, its tot al mass, and its spinning speed have to satisfy for stable hovering. The calculations presented in this paper can be used as a guide to the anal ysis and synthesis of magnetic traps for neutral particles. (C) 1999 Elsevi er Science B.V. All rights reserved.