This paper proposes a unified dynamic model for aerial robots which encompasses all known actuation principles including tilting propellers and centroid variation methods such as moving masses or robotic manipulators. Of course, one can envision a wide variety of vehicles,  all with different combinations of actuation principles. Therefore, a generalised modelling methodology for such vehicles is developed and presented in this paper. The modelling approach is verified through a comparative analysis of MATLAB simulations and laboratory experiments with a tilting propeller aerial manipulator vehicle, named Toucan. Finally, in order to fully explore and exploit the capabilities of the designed aerial manipulator, contact-based experiments with force tracking are performed using the proposed adaptive impedance controller. To demonstrate the advantages of such a vehicle, the adaptive impedance control method is used to generate position and orientation commands and achieve end-effector force tracking on a flat surface while the aerial manipulator maintains neutral attitude. This greatly increases the stability and safety of contact-based operations, as the vehicle does not require changes in attitude to meet the force requirements.