The increase in demand for performance for satellite capabilities has pushed the design of the system to be more power consuming. Currently, most of the satellite design are equipped with large solar panel in order to produce sufficient power. Thus, this translates to a higher flexibility in the satellite which makes the satellite prone to vibratory motion. The primary cause of vibratory motion in satellite is the attitude rotation. Reaction wheel is a widely used attitude rotation actuator for a satellite Commonly, the reaction wheels are configured in the tetrahedral form. This causes uneven maximum torque at any direction. Hence, an iterative optimal control method is applied using GPOPS toolbox to achieve minimum time of rotation with low level of induced vibratory motion. The optimized control is compared with the Eigen-axis Quaternion Feedback control to observe the performance of the optimal control. Depending on the direction of attitude manoeuvre, the optimal control has shown an improvement between 3.49% to 25.11% in manoeuvre time. Overall, the optimal control outperformed the traditional the Eigen-axis Quaternion Feedback control.