On the damping of a satellite motion

The motion in a circular orbit of a gravitationally oriented satellite, whose angular motions about the local vertical are damped by a roll-vee, gyrostabilizer system, is considered, wherein the pitch axis of the satellite remains perpendicular to the orbital plane. It is shown that no matter how large the initial local angular velocity of the satellite is, this velocity reaches any given smaller value in a finite time. It is also shown how it is possible to obtain a bound on this damping time.