  The joint magnetic and mechanical motion of a ferromagnetic nanoparticle in a
viscous fluid is considered within the dynamical approach. The equation based
on the total momentum conservation law is used for the description of the
mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is
utilized for the description of the internal magnetic dynamics. The exact
expressions for the particles trajectories and the power loss are obtained in
the linear approximation. The comparison with the results of other widespread
approaches, such as the model of fixed particle and the model of frozen
magnetic moment, is performed. It is established that in the small oscillations
mode the damping precession of the nanopartile magnetic moment is the main
channel of energy dissipation, but the motion of the nanoparticle easy axis can
significantly influence the value of the resulting power loss.
