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SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42
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 Title & Authors
SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42
Kula, Levent; Yayli, Yusuf;
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 Abstract
We review the algebraic structure of and show that has a scalar product that allows as to identify it with semi Euclidean . We show that a pair q and p of unit split quaternions in determines a rotation . Moreover, we prove that is a product of rotations in a pair of orthogonal planes in . To do that we call upon one tool from the theory of second ordinary differential equations.
 Keywords
hyperbolic number;split quaternion;generalized inverse;rotation;timelike plane of index 1;timelike plane of index 2;spacelike plane;
 Language
English
 Cited by
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On the Semisimilarity and Consemisimilarity of Split Quaternions, Advances in Applied Clifford Algebras, 2016, 26, 2, 847  crossref(new windwow)
17.
The Regularity of Functions on Dual Split Quaternions in Clifford Analysis, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
 References
1.
O. P. Agrawal, Hamilton operators and dual-number-quaternions in spatial kinematics, Mech. Mach. Theory. 22 (1987), no. 6, 569-575 crossref(new window)

2.
J. Inoguchi, Timelike Surfaces of Constant Mean Curvature in Minkowski 3-Space, Tokyo J. Math. 21 (1998), no. 1, 140-152

3.
L. Kula and Y. Yayli, Dual Split Quaternions and Screw Motions in Minkowski 3-space, Iranian Journal of Science and Technology (Trans A), preprint

4.
B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983

5.
P. J. Ryan, Euclidean and non-Euclidean Geometry, Cambridge University Press, Cam- bridge, 1986

6.
Y. Tain, Universal Factorization Equalities for Quaternion Matrices and their Applica- tions, Math. J. Okoyama Univ. 41 (1999), 45-62

7.
J. L. Weiner and G. R. Wilkens, Quaternions and Rotations in E4, Amer. Math. Monthly 112 (2005), no. 1, 69-76 crossref(new window)