Generalized Euler Sequences Revisited

It has previously been shown in the literature that the generalized Euler sequences (also known as Davenport sequences) provide a universal set of attitude representations. However, while these works assert the existence of generalized Euler angles for a given attitude, they do not provide explicit ranges that those angles must lie within. In addition, they do not generally provide physical insight into what a generalized Euler sequence is. This paper addresses these two points. As such, this paper contains a comprehensive self-contained treatment of generalized Euler sequences. In particular, a constructive approach is taken to proving that the generalized Euler sequences provide a universal set of attitude representations. In doing so, specific ranges that contain the generalized Euler angles are obtained, and physical insight is provided into the generalized Euler sequences. The singularity of the generalized Euler sequences is characterized, and it is shown that the generalized Euler angles are uniquely specified within their restricted ranges when away from the singularity condition.