  Floating drops of magnetic fluid can be brought into rotation by applying a
rotating magnetic field. We report theoretical and experimental results on the
transition from a spheroid equilibrium shape to non-axissymmetrical three-axes
ellipsoids at certain values of the external field strength. The transitions
are continuous for small values of the magnetic susceptibility and show
hysteresis for larger ones. In the non-axissymmetric shape the rotational
motion of the drop consists of a vortical flow inside the drop combined with a
slow rotation of the shape. Nonlinear magnetization laws are crucial to obtain
quantitative agreement between theory and experiment.
