Reorientations of Flexible Spacecraft Using Momentum Exchange Devices

Abstract : We study rest-to-rest reorientations of flexible spacecraft using momentum exchange devices. A new and concise form of the equations of motion for a rigid body containing a cluster of gimbaled momentum wheels is developed using the Euler-Newton approach. Special restrictions of the gimbaled momentum wheel equations yield equations of motion for the momentum wheel cluster and the control moment gyroscope cluster. A mathematical model of a free spacecraft with Euler-Bernoulli appendages is developed. Using the assumed modes method, a complete set of equations is developed which describes the dynamics of a spacecraft with flexible appendages and gimbaled momentum wheels. Special attention is paid to singularity problems in control moment gyro clusters. A control law based on the singular value decomposition is developed which avoids torque output commands in the nearly singular direction. The stationary platform maneuver, a maneuver along the set of equilibrium solutions of a zero angular velocity spacecraft, is extended to the control moment gyro cluster. The set of equilibria for a control moment gyro cluster is a unique surface in gimbal angle space. A control law which reorients the spacecraft while remaining close to this surface is developed using a Lyapunov method.

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