Periodic oscillation of gyrostat-satellite about its center of mass in an elliptical orbit

The motion of a satellite gyrostat with respect to the center of mass under the effect of a gravity moment in a Keplerian elliptical orbit is analyzed. The motion is described by a system of ordinary differential equations of sixth order with periodic coefficients. It is assumed that the intrinsic kinetic moment of the gyrostat is large and that the system of equations of motion contains a large parameter. An attempt is made to find symmetric periodic solutions to this system which are close to periodic solutions to a corresponding fourth-order degenerate system. The unknown solutions are obtained in series in negative powers of the large parameter, and are investigated numerically.