ON THE MOTION AND STABILITY OF A MULTIPLE CONNECTED GRAVITY-GRADIENT SATELLITE WITH PASSIVE DAMPING.

A generalized analytical method is formulated for studying the motion and stability of a gravity-gradient satellite inertially connected with one or two gimballed damping booms which are assumed to be hinged at or very near the system center of mass it is the relative motion between these connected bodies which affords a means of dissipating the librational energy. An experimental satellite, called DODGE, employing the single damper boom will be launched in 1967. The equations of rotational motion are derived using Lagranges general formulation, where the system center of mass is assumed to be in a circular orbit. Included are the effects of the gravitational restoring torques, the dissipative torques, and the gyroscopic torques that result from the coupling between the orbital angular velocity and the rotational motion in pitch-roll-yaw referenced to a local vertical frame. The equations are then linearized under suitable small angle assumptions to consider the motion and stability in the vicinity of the equilibrium point. The stability of the linear system is analyzed using both the methods of Routh-Hurwitz and Lyapunovs second or direct method. An extension of the linearized theory considers the stability of a particular nonlinear system, and examines the capture from zero inertial angular rate. Expressions are developed for the thermal deflections of the extendible booms and the torques resulting from the interaction of solar radiation forces with the bent booms. The stability criterion developed for the linear system is extended to consider the assumed continuously acting solar torques. This is achieved with an application of Malkins theorem. Author