We consider an axially symmetric satellite with a large inner angular momentum (i.e. the satellite is a gyrostat) directed along the symmetry axis. The satellite center of mass moves along a circular orbit around an attractive center, the satellite attitude motion being affected by the gravitational torque. We investigate periodic motions of the satellite symmetry axis in a vicinity of an invariable direction in the absolute space. Such motions are described by the system of differential equations of the fourth order that has periodic coefficients and contains a large parameter. We prove the unique existence of the symmetric periodic solution of the system using specific methods of large parameters.

Artificial satellite, gyrostat, periodic motions, large parameter

Theoretical and applied problems of mechanics