Nonlinear Dynamics

, Volume 32, Issue 1, pp 71-92

First online:

The Vectorial Parameterization of Rotation

  • Olivier A. BauchauAffiliated withSchool of Aerospace Engineering, Georgia Institute of Technology
  • , Lorenzo TrainelliAffiliated withDipartimento di Ingegneria Aerospaziale, Politecnico di Milano

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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 formulae needed for a complete implementation of the vectorial parameterization of rotation are included in this paper.

finite rotations parameterization of rotations