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An analytic study of flywheel autopilots for attitude control of space vehicles is described, and the results of a three-axis analog computer program are presented. The objectives of this study were to determine the requirements, capabilities and limitations of flywheel autopilots as functions of desired accuracy and speed of response, disturbing moments, differential gravity restoring torques, component uncertainties, and vehicle initial attitude and attitude rate errors. The stability and accuracy degradations that resulted from not compensating for gyroscopic crosscoupling torques are summarized. Design tools are presented for synthesizing a three-axis autopilot in accordance with specified design criteria of size, power, accuracy, response rate and error disturbances.