Three simple and efficient methods are presented for the vibration control of slewing flexible structures. The constrained motion method in two stage, CMM-TS, accomplishes the first stage rigid-body rotational maneuver by the Lagrange multiplier formulation and minimizes the flexible body vibration at the terminal state by an optimal control law. The constrained motion method with active damping, CMM-AD, employs piezoelectric actuator with velocity feedback for active damping control. The required slewing time and settling time is governed by the control torque and the control voltage, respectively. The third method, CMM-CO, combines the active damping control and the optimal torque control for vibration suppression during and after the slewing motion. All methods are shown to be efficient in computation, concise in formulation, and effective in hardware realizable application.