Review of Attitude Representations Used for Aircraft Kinematics

A detailed survey is presented 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. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Euler angles, the Euler-axis rotation parameters, the direction cosines, and the Euler-Rodrigues quaternion. The emphasis is directed at the application of the quaternion formulation to aircraft kinematics. Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Euler angle formulation, is far superior to the other commonly used formulations based on computational efficiency alone. A development of 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 case of constant rotation, is also presented