Periodic motion of a satellite-gyrostat relative to its mass center under action of a gravitational torque

We investigated the mode of satellite uncontrolled attitude motion in which an axially symmetric satellite rotated around its symmetry axis corresponding to the minimal moment of inertia whereas that axis made periodic oscillations in absolute space. We assumed the satellite orbit was circular, the satellite had inner kinetic momentum (i.e. it was a gyrostat) directed along the symmetry axis, and the satellite was affected by the gravitational torque. We studied periodic motions of the satellite symmetry axis using analytical and numerical methods. Those motionslook like the attitude motion of the satellite Foton M-3 in 2007 and some motions of the orbital station Mir in 1999 — 2000.