Abstract
In this paper the basic equations of motion for space vehicles with various passive control moment gyro (CMG) configurations are presented. As the exact equations of motion are nonlinear, linear models or linearized expressions have been established. This is of major importance especially for system design as the linearized equations allow one to determine explicitly the influence of system parameters on performance. It was found that for step and sinusoidal input functions, the errors due to linearization are less than 1%. Special attention was given to friction phenomena, i.e., viscous and Coulomb friction, which arise in connection with the motion of the CMGs about their respective gimbal axes. It was found that friction decisively influences system performance. Coulomb friction, in general, severely restricts the attitude stabilization capability of the CMGs until the space vehicle has attained a certain angular velocity.
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