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I need help with part 5B. Fig.1 shows a satellite whose pointing angle is controlled by varying the speed of a reaction wheel. The reaction

I need help with part 5B.

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Fig.1 shows a satellite whose pointing angle is controlled by varying the speed of a reaction wheel. The reaction wheel can be tought of as an electric motor with a flywheel attached to it. The angular velocity of the reaction wheel relative to the satellite can be varied by changing the voltage applied to its armature winding (electric motor). Because the reaction torque between the satellite and the motor, there is no change in the total angular momentum of the combine satellite and the motor. Thus, as the speed of the wheel relative to the satellite is varied, the angular velocity of the satellite with respect to an inertial reference frame must vary such that the total angular memonetum remain constant. Reference direction Reaction wheel Satellite Fig. 1. A satellite with a reaction wheel By drawing a free-body diagram for the satellite and the reaction wheel separately and summing the moments about the axis of rotation, the following set of state-variable equations can be obtained = 2Jea where 6: pointing angle of the satellite (rad) w: angular velocity of the satellite (rad/s) 2: speed of the reaction wheel relative to the satellite (rad/s) "m electric motor torque (Nm) B: viscous coefficient if the friction between the reaction wheel and the satellite (N.m.s/rad) Js: Moment of inertia of the satellite (kg.m) ": moment of inertia of the reaction wheel (kgm le: equivalent moment of inertia where

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