Spin-up instability of electromagnetically levitated spherical bodies

Stability of a solid sphere in both uniform and linear alternating magnetic fields is considered with respect to virtual rotations. When the frequency of the alternating magnetic field exceeds a certain critical threshold depending on the configuration of the field, the sphere is found to spin up around a horizontal axis. The physical mechanism of this instability is the same as that of operation of a single-phase induction motor. Sufficiently small rotational disturbances can be completely suppressed by imposing an axial steady magnetic field of strength comparable to that of the alternating field. Nonlinear stability analysis shows that for sufficiently high frequencies, spin-up can be caused by large disturbances even when all infinitesimal disturbances are stable.