Simple theory for the Levitron®

The Levitron® is a popular toy that provides a unique and interesting demonstration of levitation using permanent magnets. It consists of a small, spinning magnetic top and a magnetic base plate. Stable levitation is possible because of a unique coupling of the magnetic forces and torques with the gyroscopic action of the top. A simple theory of its operation, using a general axisymmetric form for the magnetic field of the base, is based on the dipole force model. With this model, the stable behavior of the spinning, levitated top may be investigated by testing various assumptions for its orientation. Stability is not possible if the top remains rigidly parallel to the axis of the base. On the other hand, if one assumes that the top remains aligned parallel to the local magnetic field during radial excursions, then stability is possible. This simple model, combined with measurements of the magnetic field along the axis, permits fairly accurate prediction of the upper and lower limits of the locus of stable equilibria.