Momentum Transfer in Two-Rotor Gyrostats

The orientation of a spacecraft can be changed efficiently by transferring angular momentum between the platform and internal momentum wheels using internal torques. The speed of such maneuvers depends on the size of the internal torques and may be limited by the effects of excitation of any flexible elements of the spacecraft. The internal torques required to accomplish such maneuvers arise in various forms. Three types of torque are considered: constant torques for a simple momentum transfer, viscous torques attributable to bearing friction, and time-varying torques defined by a suitable control law. A previously developed graphic result for single-rotor gyrostats is extended to the multiple-rotor case and used to illustrate the different trajectories for the two-rotor gyrostat. A novel feature is the development of stationary-platform rotational maneuvers in which the platform's angular velocity is small throughout the maneuver. These maneuvers are based on a simple control law and are not restricted to small angles. T is possible to reorient a torque-free rigid body by transferring angular momentum between the body and internal momentum wheels or rotors using internal torques. If the rotors are axisym- metric and constrained to relative rotation about their symmetry axes, then the system is called a gyrostat, and as described below, some analytical results are available. If the rotors are asymmetric, unbalanced, or both, then resonances may occur that increase the likelihood of failure of a momentum transfer maneuver, especially if the internal torques are small. These failures have been studied by numerous researchers.1 Several aspects of momentum transfer in two-rotor gyrostats are studied here. We consider three specific cases: both rotors torqued by constant-torq ue motors; one rotor torqued by a constant-torque motor with the other experiencing only a viscous damping torque; and both rotors subject to time-vary ing torques based on a simple control law. The time-varying torque control law is based on a novel approach that leads to stationary-platform maneuvers. The control law makes possible large-angle rotational maneuvers in which the angular velocity of the body remains small throughout the maneuver. Momentum-transfer approaches involving gyrostat models have been developed by many researchers. Anchev2 derived a control law for maneuvering a three-rotor gyrostat from the gravity-gradient equilibrium orientation to one of the orbiting gyrostat equilib- ria. Barba and Aubrun3 used an energy approach to describe the spinup maneuver for an axial gyrostat with constant internal torque. Hubert4'5 extended their work with the addition of energy dissipa- tion by a viscously damped rotor. Vigneron and Staley6 designed a switching control strategy to minimize the final nutation angle. Hall and Rand7 reduced the spinup problem for axial gyrostats to the study of a single first-order equation. Hall extended this to in- clude arbitrary rotor alignment8 and later to include multiple rotors.9 Hall9 also includes a survey of the literature on momentum transfer. Krishnan et al.10 studied the control of a zero-momentum two-rotor gyrostat. A large body of work on the optimal control of momentum transfer has been contributed by Junkins and colleagues. Much of this work is combined in a consistent notation in the monograph by Junkins and Turner.) * In particular, they compare Barba and Aubrun's maneuver3 with an optimal control solution that minimizes the final angular velocity of the platform and the total control torque.11 The two