Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E42

  • Kula, Levent (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE ANKARA UNIVERSITY) ;
  • Yayli, Yusuf (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE ANKARA UNIVERSITY)
  • Published : 2007.11.30
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Abstract

We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.

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References

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