In this paper we propose a controller, based on an extension of Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) framework, for shaping the whole physical characteristics of a quadrotor and for obtaining a desired interactive behavior between the robot and the environment. In the control design, we shape the total energy (kinetic and potential) of the undamped original system by first excluding external effects. In this way we can assign a new dynamics to the system. Then we apply damping injection to the new system for achieving a desired damped behavior. Then we show how to connect a high-level control input to such system by taking advantage of the new desired physics. We support the theory with extensive simulations by changing the overall behavior of the UAV for different desired dynamics, and show the advantage of this method for sliding on a surface tasks, such as ceiling painting, cleaning or surface inspection.