On the Stability of Steady Rotation of a Satellite around the Normal to the Orbital Plane

Abstract

We study the rotational motion of a satellite (a rigid body) around the center of mass in a central Newtonian gravitational field in a circular orbit. The stability problem of a steady motion is solved for the case when the symmetry axis of the satellite is perpendicular to the orbital plane, and the satellite itself rotates about the symmetry axis with a constant angular velocity (cylindrical precession). The problem depends on two parameters, the dimensionless value of the absolute angular velocity of rotation of the satellite and the ratio of its axial and equatorial moments of inertia. The rigorous stability and instability conclusions were obtained for the parameter values that were not previously studied. Together with the known results of domestic and foreign authors, these conclusions give a rigorous and complete solution to the stability problem of the cylindrical precession of the satellite in a circular orbit for all values of the problem parameters.