Parabolic approximation to EMA motion profiles

Parabolic curves fit physical trajectories well because of the inherent smoothness of inertial movement; and, with only a few parameters, they can fit complex paths far more effectively than linear approximations. This paper presents a method using parabolas to approximate the motion profiles to be used in driving an electromechanical aircraft actuator. This method allows the actuator to run longer tests more efficiently. The details of the scheme are explained with emphasis on its matrix manipulation and the fidelity of the approximation to the original, complex profile.