Spin stabilized magnetic levitation

[attachment=16500]

INTRODUCTION
The Levitron®1 ~Ref. 1! is a remarkable toy which levitates
in air a 22-g spinning permanent magnet in the form of
a small handspun top. The top is spun on a lifter plate on a
permanent magnet base and then raised to the levitation
height. The top floats about 3.2 cm above the base for over 2
min until its spin rate declines due to air resistance to about
1000 rpm. Unlike an earlier magnet toy which requires a
thrust bearing plate to stabilize motion along one direction


HOW IT WORKS
First, it is instructive to see how this trap for magnetic
dipoles doesn’t work. It is not enough to simply stabilize the
top/dipole against flipping. We can consider this the infinite
spin case,



MATERIALS TO EXPERIMENT WITH
Base magnets can be ring magnets or an array of barrel,
bar, or disk magnets. Usable large ~10-cm o.d.! ring magnets
can be found on speakers or in microwave oven magnetrons.
~It is not easy to remove ring magnets from speakers. Sometimes
the glue will release in boiling water but not always.!
If broken speakers or magnetrons are not available, four bar
magnets arranged in a square with their north poles inward,
or barrel magnets arranged in a square or circle with their
north poles up can be used


APPENDIX A: LINEAR PRECESSING MODEL
To derive the upper spin limit for the top and some of the
other dynamics, we need to go back to the equations of motion.
While our computer solution of the equations of motion
keeps terms to second order, the upper spin frequency condition
can be derived from the linearized equations