Abstract
This work presents a complete formulation of the representationand parameterization of frame motion as a tool to derive, in aconvenient form, the kinematic and dynamic governing equations ofmechanical systems characterized by both position and orientationfields. Typical applications are rigid bodies, beams, shells, andmultibody systems. The description of such systems may be performedusing compact 4-D and 6-D matrix representations, leading to theextension of many of the well-known concepts and properties of rotationsto the group of rigid displacements. Two parameterization procedures arefully developed in connection to the proposed representations: theexponential map of motion and Cayley's parameterization. Both allow fora consistent, unified treatment of the coupled linear and angularcomponents of motion. This approach entails remarkable algorithmicimplications.
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Borri, M., Trainelli, L. & Bottasso, C.L. On Representations and Parameterizations of Motion. Multibody System Dynamics 4, 129–193 (2000). https://doi.org/10.1023/A:1009830626597
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DOI: https://doi.org/10.1023/A:1009830626597