O.A. Bauchau, L. Trainelli
The
Vectorial Parameterization of Rotation
Nonlinear Dynamics, 32
(1): 71–92 (2003).
Abstract
The
parameterization of rotation is the subject of continuous research and
development in many theoretical and applied fields of mechanics, such as rigid
body, structural, and multibody dynamics, robotics, spacecraft attitude
dynamics, navigation, image processing, and so on. This paper introduces the
vectorial parameterization of rotation, a class of parameterization techniques
encompassing many formulations independently developed to date for the analysis
of rotational motion. The exponential map of rotation, the Rodrigues, Cayley,
Gibbs, Wiener, and Milenkovic parameterization all are special cases of the
vectorial parameterization. This generalization parameterization sheds
additional light on the fundamental properties of these techniques, pointing
out the similarities in their formal structure and showing their
inter-relationships. Although presented in a compact manner, all of the formulæ
needed for a complete implementation of the vectorial parameterization of
rotation are included in this paper.