M. Borri, L.
Trainelli, C.L. Bottasso
On
Representations and Parameterizations of Motion
Multibody System Dynamics, 4:
123-193 (2000).
Abstract
This work presents a complete formulation of the
representation and parameterization of frame motion, as a tool to derive in a
convenient form the kinematic and dynamic governing equations of mechanical
systems characterized by both position and orientation fields. Typical
applications are rigid bodies, beams, shells, and multibody systems. The
description of such systems may be performed using compact 4-D and 6-D matrix
representations, leading to the extension of many of the well known concepts
and properties of rotations to the group of rigid displacements. Two
parameterization procedures are fully developed in connection to the proposed
representations: the exponential map of motion and Cayley's parameterization.
Both allow for a consistent, unified treatment of the coupled linear and
angular components of motion. This approach entails remarkable algorithmic
implications.