SYMMETRICAL OSCILLATIONS IN ATTITUDE MOTION OF GYROSTAT IN WEAK ELLIPTICAL ORBIT IN GRAVITATIONAL AND MAGNETIC FIELDS
A gyrostat in central New toniangravitational ﬁeld and dipolarmagnetic ﬁeldisconsidered. The gyrostat is moving along weak elliptical Keplerian orbit lying in magnetic equatorial plane. 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 in the case of the circular orbit the system of diﬀerential equations of gyrostat attitude motion is reversible with three stationary sets. Moreover, this system may be reduced to quadratures by constructing four ﬁrstintegrals which existunder certain assumptions about the presence of a dynamic and electromagnetic symmetry ofgyrostat.In moregeneral case of weak elliptical orbit the mentioned reductionisim possible, butthediﬀerential system preserves its reversibility. The symmetrical periodic motions of oscillatory type are analyzed. The absence of doubly symmetric solutions is proved. 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. Refs 9.