Circumventing an essential singularity in attitude dynamics

Elipe A.

University of Zaragoza, Spain

As it well known in attitude dynamics, the Eulerian angles (\phi, \theta, \psi) cannot afford a regular representation of the group SO(3) for they are singular for \theta = 0. Several representations have been derived to avoid this singularity that is essential. The Cartan representation avoids this singularity, although it creates a new one. The same happens with other representations, such as Serret--Andoyer angles. Quaternions of unit length representation is free of this singularity, but there are still an ambiguity in the sign.

In this communication, we provide a canonical formalism for the Cartan angles, and from it, a set of Serret--Andoyer type variables and a canonical set of unit quaternions are obtained.