Gyroscopic Stabilization of Passive Magnetic Levitation

A nonlinear mathematical model able to describe the motion of a passive magnetic levitation device, known as Levitron, is presented in this paper. Using the standard approach usually applied in rotordynamics and without introducing any preliminary assumptions, the equations of motion for all six degrees of freedom of the magnetic spinning top are obtained. By computing the four natural frequencies characterizing the horizontal translational vibrations of the rotor and the whirling motion of its axis, the conditions for stable levitation in terms of the spin speed are obtained. Some results coming from the numerical integration of the equations of motion are also presented and compared with those obtained using the simplified model based upon the fast top assumption.