The earth-scanning satellite is in a circular orbit of p period The angular velocity of...

The earth-scanning satellite is in a circular orbit of p period The angular velocity of the satellite about its y- or pitch-axis is and the angular rates about the x- and z-axes are zero. Thus, the x-axis of the satellite always points to the center of the earth. The satellite has a reaction-wheel attitude-control system consisting of the three wheels shown, each of which may be variably torqued by its individual motor. The angular rate of the z-wheel relative to the satellite is at time t = 0, and the x- and y-wheels are at rest relative to the satellite at t = 0. Determine the axial torques Mx, My, and Mz which must be exerted by the motors on the shafts of their respective wheels in order that the angular velocity ω of the satellite will remain constant. The moment of inertia of each reaction wheel about its axis is I. The x and z reaction-wheel speeds are harmonic functions of the time with a period equal to that of the orbit. Plot the variations of the torques and the relative wheel speeds as functions of the time during one orbit period. (Hint: The torque to accelerate the x-wheel equals the reaction of the gyroscopic moment on the z-wheel, and vice versa.)