SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42

Title & Authors
SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42
Kula, Levent; Yayli, Yusuf;

Abstract
We review the algebraic structure of $\small{\mathbb{H}{\sharp}}$ and show that $\small{\mathbb{H}{\sharp}}$ has a scalar product that allows as to identify it with semi Euclidean $\small{{\mathbb{E}}^4_2}$. We show that a pair q and p of unit split quaternions in $\small{\mathbb{H}{\sharp}}$ determines a rotation $\small{R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}}$. Moreover, we prove that $\small{R_{qp}}$ is a product of rotations in a pair of orthogonal planes in $\small{{\mathbb{E}}^4_2}$. 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
1.
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