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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 15 | Number 2 | Year 2014 | Article Id. IJMTT-V15P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V15P512

Dual Transformations and Instantaneous Screw Axes


Gülsüm YÜCA, Yusuf YAYLI
Abstract

In this study, we investigate instantaneous screw axes with the help of a dual transformation which is defined in [1]. This transformation makes clear the relations between Euclidean space and Lorentzian space. The aim of this paper is to observe instantaneous screw axes under this dual transformation.

Keywords
Dual transformation, space motion, instantaneous screw axis
References

[1] R. Dohi, Y. Maeda, M. Mori and H. Yoshida, “A dual transformation between SO(n+1)\{a00=0} and SO(n,1) and its geometric applications”, Linear Algebra and its Applications. 432, 770-776, 2010.
[2] G. Yüca and Y. Yaylı, “Kinematics of dual transformation”, European International Journal of Science and Technology, Vol.3 No.8, October 2014.
[3] R. López, “Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space”, arXiv:0810.3351v1 [math.DG], 2008.
[4] O.Neill, “Semi-Riemannian Geometry”, Pure and Applied Mathematics. 103, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983.
[5] J. M. McCarthy, “An Introduction to Theoretical Kinematics”, MIT Press, Cambridge, 1990.
[6] A. Karger, J. Novak, “Space Kinematics and Lie Groups”, Gordon and Breach Science Publishers, New York, London, Paris, Montreux, Tokyo 1985.
[7] Ç. Ramis and Y. Yaylı, “Dual split quaternions and Chasles’ theorem in 3-dimensional Minkowski Space Adv. Appl. Cli¤ord Algebras. 432, 770-776, 2010.
[8] Y. Yaylı, A. Çalıskan, and H. H. Uğurlu, “The E. Study maps of circles on dual hyperbolic and Lorentzian unit spheres and ”, Math. Proc. R. Ir. Acad. 102A, no. 1,37-47, 2002.

Citation :

Gülsüm YÜCA, Yusuf YAYLI, "Dual Transformations and Instantaneous Screw Axes," International Journal of Mathematics Trends and Technology (IJMTT), vol. 15, no. 2, pp. 93-97, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V15P512

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