On representations and parameterizations of motion

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.