Elliptical rotations with hybrid numbers

İskender Öztürk () and Mustafa Özdemir ()
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İskender Öztürk: Akdeniz University
Mustafa Özdemir: Akdeniz University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 23-39

Abstract: Abstract In this article, some geometric interpretations and applications of hybrid numbers, which unify elliptic, hyperbolic and dual numbers, are given. First, the definition of an elliptical (complex) plane is given, and elliptic rotations in this plane are examined using hybrid number multiplication. Also, mutually orthogonal planar elliptical rotations in four-dimensional space are discussed. At last, matrix forms of a non-parabolic rotation transformation are expressed, and Rodrigues and Cayley rotation transformations for an elliptical hybrid vector are proved.

Keywords: Elliptical rotations; Hybrid Numbers; Split quaternions; Coquaternions; 70B05; 70E18; 83C65; 11R52 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00343-5

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