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 develop ment of the aircraft kinematic transformation equations in terms of four di fferent attitude representations, including the well-known Enter angles, th e Euler-axis rotation parameters, the direction cosines, and the Euler-Rodr igues quaternion. The emphasis is directed at the application of the quater nion formulation to aircraft kinematics. Results are presented that reinfor ce observations that the quaternion formulation, typically implemented to e liminate singularities associated with the Enter angle formulation, is far superior to the other commonly used formulations based on computational eff iciency alone. A development of quaternion constraints necessary to indepen dently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azim uth angle is presented. For verification of simulation codes, a general clo sed-form solution to the quaternion formulation, for the case of constant r otation, is also presented. Additionally, a discussion is provided of numer ical integration methods and numerical errors for the quaternion formulatio n. This discussion is especially important for simulations that may still u tilize a common error reduction scheme originally developed for analog comp uters.