Abstract
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 nonaxisymmetrical three-axis 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 nonaxisymmetric 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.