On symmetrical oscillations of gyrostat in weak elliptic orbit

A gyrostat in weak elliptical Keplerian orbit lying in geomagnetic equatorial plane is considered. The gyrostat is supplied with flywheel and possesses electrostatic charge and intrinsic magnetic moment. The gyrostat attitude motion under the action of Lorentz and magnetic torques is under consideration. It was revealed that the differential system of gyrostat attitude motion is reversible with three stationary sets. The symmetrical periodic motions of oscillatory type are analyzed. A bifurcation in the set of gyrostat symmetrical oscillations and generation of two isolated symmetrical oscillations is discovered in transition from circular orbit to elliptical one.