Stability analysis of a paramagnetic spheroid in a precessing field

The stability of a paramagnetic prolate or oblate spheroidal particle in a precessing magnetic field is studied. The bifurcation diagram is calculated analytically as a function of the magnetic field frequency and the precession angle. The orientation of the particle in the synchronous regime is calculated. The rotational dynamics and the mean rotational frequency in the asynchronous regime are also obtained. The theoretical model we describe enables the analytic calculation of the dynamics of the particle in the limiting case when the motion is periodic. The theoretical models were also compared with experimental results of rod like particle dynamics in a precessing magnetic field. The experimental results are in good agreement with the proposed theory.