Symmetrical oscillations in attitude motion of gyrostat in weak elliptical orbit in gravitational and magnetic fields

Abstract

A gyrostat in central Newtonian gravitational field and dipolar magnetic field is considered. 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 first integrals which exist under certain assumptions about the presence of a dynamic and electromagnetic symmetry of gyrostat. In more general case of weak elliptical orbit the mentioned reduction is impossible, but the differential 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.

Keywords:

gyrostat, weak elliptical orbit, attitude motion, magnetic field, reversible system, stationary set, oscillations, bifurcation