The Levitron is a magnetised top, which can achieve
magnetic levitation when spun and initially lifted above a magnetic
base. The Levitron will "float in the air" for several minutes, which
is impressive to watch. A video showing the trick is
here.
A Senior Physics student doing a Special Project wrote codes to model
the Levitron, numerically solving the "fast top" equations of motion
(see e.g. Simon et al. 1997, American J. Phys. 65, 286292). I used
the codes to produce the animations linked to below.
Modeling
Simulation with angular speed 150 rad/sec
 stability
Simulation with angular speed 210 rad/sec
 instability
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