Abstract
In this paper, we provide a brief analysis of second-order skew-symmetric Cartesian tensors and present some of their applications in the analysis of spatial rotations. In particular by exploring various relationships between second-order skew-symmetric Cartesian tensors and their vector invariants, we provide a number of important tensor identities which enable us to manipulate effectively (and thus simplify) other complex tensor equations. Also, based on relatively oriented skew-symmetric second-order Cartesian tensors, we provide an analysis for the orientations of spatial rotations and derive some important formulations for their axes and the angles of rotation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Angeles, Rational Kinematics, Springer-Verlag, New York, 1988.
W. H. Greub, Linear Algebra, Springer-Verlag, New York, 1967.
D. Hestenes, New Foundations of Classical Mechanics, D. Reidel Publishing Company, Dordrecht, Holland, 1986.
H. Goldstein, Classical Mechanics, Reading, MA:, Addison Wesley, 1980.
J. Stuelpnagel, “On the Parametrization of the Three-Dimensional Rotation Group”, SIAM REVIEW, Vol. 6, No. 4, pp. 422–430, October 1964.
C. A. Balafoutis, and R. V. Patel, “A Cartesian Tensor Methodology for the Study of Classical Newtonian Dynamics, Part I: Cartesian Tensor Analysis,” in Proc. 10th Symposium on Engineering Applications of Mechanics, pp. 55–60, Kingston, Ontario, May 27–30, 1990.
C. A. Balafoutis and R. V. Patel, Dynamic Analysis of Robot Manipulators: A Cartesian Tensor Approach, Kluwer Academic Publishers, Boston, MA, 1991.
A. M. Goodbody, Cartesian Tensors: With Applications to Mechanics, Fluid Mechanics and Elasticity, Ellis Horwood, England, 1982.
A. Lichnerowicz, Elements of Tensor Calculus, Methuen, London, 1962.
R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications, John Wiley & Sons, New York, 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Balafoutis, C.A., Patel, R.V. (1992). The Use of Skew-Symmetric Cartesian Tensors in Describing Orientations and Invariants of Spatial Rotations. In: Tzafestas, S.G. (eds) Robotic Systems. Microprocessor-Based and Intelligent Systems Engineering, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2526-0_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-2526-0_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5115-6
Online ISBN: 978-94-011-2526-0
eBook Packages: Springer Book Archive