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3) The illustrated spacecraft (right) contains a 4-for-3 array of reaction wheels. a) What are the maximum spacecraft rates (x, wy and wz ) if all wheels are operating and the spacecraft's net momentum is zero? Express your answers in degrees /second. b) What is the spacecraft's maximum Z-axis > angular rate, if the -Y wheel has failed? Assume that the spacecraft's net momentum is zero. Express your answer in degrees/second. Ay X c) If the spacecraft's initial conditions are ®x B (4 places) = wy = QZ = 0 and wheel momentum is as illustrated below, what is the maximum possible spacecraft rate about the Z axis? Each one of four identical reaction wheels has the following capabilities: H = + 60 ft-lb-sec Z T = I 42 oz-in The reaction wheels are arranged in a pyramid 15 ft-lb-sec configuration as shown above, with ß =30 deg. Spacecraft moments of inertia are: Ixx = 500 sl-ft2 Gy X Iyy = 500 sl-ft² Izz = 700 sl-ft² Products of inertia = 0

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