The mathematics of the Levitron^®

The Levitron is a fascinating toy consisting of a magnet in the form of a spinning top which can float stably above a repelling magnetic base.

Details of the toy can be found here.

I have made a 3-minute video of the levitron in action. I also have a levitron in my office, and if contacted in advance, I would be happy to demonstrate.

The aim of the project is to understand the why the Levitron works by modelling it mathematically as a lagrangian dynamical system with symmetries. This is achieved by studying the two papers listed below.

References

1. The Levitron^TM: an adiabatic trap for spins
   Michael Berry
   Proc. R. Soc. Lond. A 452 (1996) 1207-1220.
2. Stability of Levitrons
   Holger Dullin and Robert Easton
   Physica D 126 (1999) 1-17.

Both of these papers are available electronically from the University of Edinburgh Library.