Stationary resonant pitching motions of a controlled satellite.

Abstract

A controlled satellite moving in a slightly elliptical orbit, with one axis of the satellite perpendicular to the orbit plane, is considered. The control system involves two single-degreeof-freedom gyroscopes in a so-called roll-vee configuration. The stationary, resonant, nonlinear oscillatory and rotary states, and their stability, are determined, under the assumption that the eccentricity of the orbit and the gyro damping rate are sufficiently small. Both forward and retrograde rotations are considered. It is found that the stable stationary states are strictly stable, rather than neutrally so as in the case of an uncontrolled satellite. The gimbal angle is zero, in the lowest-order approximation, for the stationary oscillatory states. For the forward stationary rotary states, the gyro gimbals are partially collapsed towards the pitch axis. For the retrograde stationary rotary states, the gyro gimbals are spread away from the pitch axis, and unless the nominal roll-vee angle is less than a certain quantity, the gyro gimbals will be against the yaw stops, which is not permitted by the analysis.