We derive equations of motion for paramagnetic and ferromagnetic particles
fully accounting for gyromagnetic effects. Considering the Einstein-de Haas
effect for an ellipsoidal paramagnetic particle we find that starting from a
quiescent non-magnetized state, after the field is switched on a rotation along
the short axis is established. This is confirmed by the stability analysis of
the fixed points of the corresponding ordinary differential equations. In the
case of a ferromagnetic particle we integrate the equations of motion in the
dissipationless case by finding the integrals of motion. We also reformulate
the equations in a Hamiltonian framework in this case and find a period of
small nutation oscillations.Comment: 24 pages, 15 figure