Optimum Design of a Gravitationally Oriented Two-Body Satellite

The dynamics analysis by Fletcher, Rongved, and Yu l has shown that a two-body satellite will achieve an earth-pointing motion from an initial tumbling as a result of energy dissipation in the hinge joint through the relative motion between the two bodies. For a practical application, we shall consider the earth-pointing body to be like a dumbbell and the auxiliary body like a sheet, the two being connected to each other through a hinge mechanism of universal-joint type to allow a two-degree-of-freedom relative motion. When the satellite is in an earth-pointing motion, the auxiliary body is parallel to the local horizontal in its unstable orientation, and the two axes of relative motions are aligned with the roll and pitch direction (see Fig. 1). The overall aspect of such a passive gravitational attitude control system has been studied by Paul, West, and Yu 2 employing the magnetic hysteresis damping mechanism. Certain designs of the satellite in terms of moments of inertia, spring constants, and damping constants have been given in both Refs. 1 and 2 for an altitude of 6000 nautical miles (nm). They 49