Wave-based control is a relatively new approach which has already been applied successfully to control a range of under-actuated, flexible mechanical systems, such as robots and cranes, through a rest-to-rest manoeuvre after it identifies, then measures and finally exploits the propagation time delay effects inherent in flexible systems. In this technique, the actuator motion is directly controlled in a way that, simultaneously, indirectly controls the motion of the attached flexible systems, thereby combining position control and active vibration damping. A significant development of this strategy is here presented, in which the directly controlled actuation variable is force (or torque) rather than position or motion, as before. This new formulation is particularly relevant for motion control of systems whose actuators are not grounded, such as spacecraft, with thrusters, reaction wheels or magnetic torquers, where the natural, actuator input variable is a force or torque, to be specified by the control law (rather than actuator motion). This development considers a real (non-ideal) actuator with significant inertia and thus associated time delay in responding to input signals. The new control design approach is presented, and applied to planar, translation and rotation (slewing) of an approximate model of a spacecraft having two flexible appendages, representing for example, solar panel arrays or antennas, modelled as systems of lumped masses and springs, with (possibly) different appendages on one spacecraft. Despite the dynamic complexity of the multiple attached flexible arrays, having many degrees of freedom, with complex vibration modes, and use of a non-ideal, ungrounded actuator, the proposed control strategy can achieve precise motion control, whether translation, rotation or both, while actively suppressing vibrations of the flexible appendages.