Periodic solutions in model of pulsar rotation

The model of pulsar rotation is suggested that considers magnetic properties of the core and asynchronous rotation of the core and shell. The model is applicable within a finite time period in the interval between two ''starquakes'' when one may neglect the energy losses for viscous friction and electromagnetic radiation. It is assumed in the model under consideration that: a) the pulsar shell is absolutely hard. The liquid core with a constant density fills up the ellipsoidal cavity; b) the shell rotation is determined by the orthogonal matrix. The liquid motion in the cavity is described by the magnetohydrodynamics equations; c) the electromagnetic field has a break at the liquid-shell interface on both sides of which the magnetic field contacts the ellipsoid surface and is frozen in the medium. The values of the surface current, surface charge and elastic pressure on the side of the shell are determined from the conditions at the magnetic hydrodynamics break. The magnetic force lines in the shell are closed up through the surrounding vacuum. Periodic solutions being in agreement with astrophysical data have been found