This article addresses the problem of the modeling and control of an Unmanned Aerial System (UAS) that consists of a UAV carrying a robotic manipulator. The dynamics of the UAS are derived based on the recursive Newton-Euler equations in order to handle the floating-base effect. Accordingly, the dynamics account for the force and torque transferred from the base of the manipulator to the UAV and the translational and angular velocities and accelerations from the UAV to the manipulator. The integrated nonlinear dynamic equations are symbolically derived and efficient code for execution at embedded systems is generated. An efficient nonlinear control scheme regulates the states of the UAS to a desired configuration. Simulation results are provided to evaluate the performance of the developed strategy, in comparison to the ones derived by simplifying the coupling of the UAV and manipulator dynamics by considering only the spatial coordinates of the center of mass of the manipulator.