Generalized Split Quaternions and Their Applications on Non-Parabolic Conical Rotations

Duru M., ÇOLAKOĞLU H. B.

Symmetry, cilt.15, sa.9, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 9
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/sym15091805
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Lorentzian inner product, Lorentzian rotation matrix, Lorentzian symmetry, Lorentzian vector product, split quaternion
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which is a generalized Lorentzian sphere, non-parabolic conical rotations with nonnull axes are expressed using the generalized split quaternions with supporting numerical examples.