On the Rotation of a Spacecraft Carrying a Deformable Antenna in the Gravitational Field of Force

Abstract

The problem of motion, relative to the center of mass, of a satellite rotating around the center of gravity over an elliptical orbit, is studied. The satellite consists of axisymmetric solid and viscoelastic sections, with the viscoelastic section being a hemispherical antenna. It is shown that the evolution of satellite rotations can be subdivided into two stages; fast, caused by deformations under an effect of inertia forces, and slow, or the dissipative stage. It is shown that the fast evolution stage consists in the fact that the angular momentum vector is located along the satellite’s axis of symmetry (in this case, the axial moment of inertia is greater than the equatorial), and in the equatorial plane of the ellipsoid of inertia (if the equatorial moment of inertia is greater than the axial). The slow evolution stage was considered for the case where the axial moment of inertia is greater than the equatorial. It is found that slow evolution consists in decelerating the axial rotation and in the angular momentum vector inclining to the orbital plane.