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, 286-292). 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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