Elliptical rotations with hybrid numbers

Öztürk İ., ÖZDEMİR M.

Indian Journal of Pure and Applied Mathematics, vol.55, no.1, pp.23-39, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s13226-022-00343-5
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Page Numbers: pp.23-39
  • Keywords: 11R52, 70B05, 70E18, 83C65, Coquaternions, Elliptical rotations, Hybrid Numbers, Split quaternions
  • Akdeniz University Affiliated: Yes

Abstract

© 2022, The Indian National Science Academy.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.