(Solved): Satellite usually require attitude control to ensure that the solar panels, sensor and antennas a ...

Satellite usually require attitude control to ensure that the solar panels, sensor and antennas are properly oriented. Consider the figure of a satellite below. The location of the center of mass of the satellite is marked with the orange dot. The current orientation of the satellite is \( \theta \) as shown. Thrusters are attached to the satellite which can apply a desired force \( f \) as shown. The distance of the thursters from the center of mass is \( d \). The satellite can also experience disturbance (due to solar wind etc) in form of a moment \( M_{d} \) applied at its center of mass. Obtain the equations of motion (differential equations) of the rotational dynamics of the satellite.