Stability of the Levitron

abstract. Abstract text lines The Levitron, manufactured by Fascinations in Seattle WA, successfully demonstrates magnetic suspension. A 22 gram spinning magnetic dipole top is supported by magnetic forces that balance its weight about 3.2 cm above a magnetized base, and it will float about two minutes until its spin rate has declined to about 1000 rpm. However, since in general i t is not possible (The Feynman Lectures on Physics Volume II, 5-4) to have a potential energy minimum or maximum for any rigidly connected system of poles in a magnetic field, the stability of the Levitron is not obvious. Gyroscopic forces that prevent the top from flipping over and being attracted to the base have been suggested as the source of the stability (US Patent 5,404,062, Hones et al.). We find that fixing the direction of the top axis in space is not sufficient. An analysis and numerical integration of the five degree of freedom equations of motion of the top that includes gyroscopic precession around the local magnetic field lines do predict that the top will be supported stably up to spin speeds of 2100 rpm.