Supplementary Active Stabilization of Nonrigid Gravity Gradient Satellites

EACTION jets are one of the methods for augmenting the dynamics of satellites whose attitude nominally is stabilized by gravity gradient (GG) forces and a passive damper. The present study differs from previous ones on attitude control by jets in two main ways: 1) It includes nonrigidity, and 2) it uses the Hamiltonian H to develop the control laws. Consideration of nonrigidity is necessary when active control forces are applied to vehicles with flexible parts, such as the inertia booms usually needed on GG satellites. Previous use of H in satellite studies has been concerned largely with its application as a Lyapunov function in stability investigations of passive vehicles. Contents Let H be the Hamiltonian of the GG satellite's state x under the Keplerian orbit approximation, x defines the attitude displacement and rate relative to the local vertical-orbit pole cartesian frame R and, if the satellite is nonrigid, the relative motions of its parts. The potential energy terms included in H result from internal stiffness and the first-order component of the central force gravity field. Assume that the satellite contains no parts whose motions are not constrained by stiffness forces, that no active alteration of the mass distribution is performed, and that all three principal moments of inertia are unequal. If disturbances Qds and orbit eccentricity e are negligible, it then will possess time-invariant stable equilibrium states xse. A constant Ku can be added to make H = 0 when x = xse. Then H > 0 when x ^ xse. H thus can serve as a measure of the displacement of x from xse. If internal damping forces Qdm are negligible, H is constant when Qds, e, and the jet forces u are zero, since it then is not an explicit function of time. Qdm yields H < 0, Qds and e can produce bounded variations in H and, under some conditions, secular growth. The purpose of u can be regarded as being to supplement Qdm by reducing H or maintaining it small. Depending on the application, it may be necessary to supplement control criteria based on H by constraints to prevent alteration of the orbit or to limit the magnitudes of critical structural vibration modes. If the satellite is tumbling at the start of the jet operation and not all the xse's are suitable for the mission, a constraint is needed on the xse about which capture is achieved. The total time derivative H of H can be put in the following form