Stability of the LevitronTM
نویسندگان
چکیده
The Levitron TM is a magnetic spinning top which can levitate in the constant eld of a repelling base magnet. An explanation for the stability of the Levitron TM using adiabatic approximation has been given by M.V. Berry. In experiment the top eventually looses stability at a critical spin rate which can not be predicted by Berry's approach. The present work develops an exact theory of the Levitron TM with six degrees of freedom which allows for the calculation of the critical spin rate. The main result is a complete classiication of possible Levitrons that allow for an interval of stable spin rates. Stability of the relative equilibrium is lost in Hamiltonian Hopf bifurcations if either the spin rate is too large or too small.
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