Question 10.11: The communications satellite is in a circular earth orbit of...
The communications satellite is in a circular earth orbit of period T. The body z axis always points towards the earth, so the angular velocity about the body y axis is 2π/T. The angular velocities about the body x and z axes are zero. The attitude control system consists of three momentum wheels 1, 2 and 3 aligned with the principal x, y and z axes of the satellite. Variable torque is applied to each wheel by its own electric motor. At time t = 0 the angular velocities of the three wheels relative to the spacecraft are all zero. A small, constant environmental torque M_{0} acts on the spacecraft. Determine the axial torques C^{(1)},C^{(2)} and C^{(3)} that the three motors must exert on their wheels so that the angular velocity \omegaof the satellite will remain constant. The moment of inertia of each reaction wheel about its spin axis is I.
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