  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 find
conditions which the height of the hovering top above the base, its total mass,
and its spinning speed have to satisfy for stable hovering. The calculation
presented in this paper can be used as a guide to the analysis and synthesis of
magnetic traps for neutral particles.
