We present a control methodology for underactuated aerial manipulators that is both easy to implement on real systems and able to achieve highly dynamic behaviors. The method is composed by two parts: i) a nominal input/state trajectory generator that takes into account the full-body dynamics of the system exploiting its differential flatness property; ii) a decentralized feedback controller acting on the actuated degrees of freedom that confers the needed robustness to the closed-loop system. We demonstrate that the proposed controller is able to precisely track dynamic trajectories when implemented on a standard hardware. Comparative experiments clearly show the benefit of using the nominal input/state generator.