A review of attitude kinematics for aircraft flight simulation

Abstract

This paper presents the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the wellknown Euler angles, the Euler-axis rotation parameters, the direction cosines and the Euler-Rodrigues quaternion. The emphasis of the paper is directed at the application of the quaternion formulation to aircraft flight simulation. Results are presented which reinforce the observation that the quaternion formulation, typically implemented to eliminate the singularities associated with the Euler angle formulation, is far superior to the other commonly used formulations based on computational efficiency alone. A development of the quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verification of simulation codes, a general closed-form solution to the quaternion formulation, for the special case of constant rotation, is also presented. Additionally, the paper provides a discussion of the numerical integration of the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers. The paper includes a detailed review of the literature on attitude representation dating from the early work of Euler and Hamilton to recent publications in fields such as navigation and control. Nomenclature