Elliptic and Hyperbolic Rotational Motions on General Hyperboloids

Çolakoğlu H. B., Duru M.

Symmetry, cilt.17, sa.6, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17060845
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Anahtar Kelimeler: Cayley transformation, Householder transformation, Lorentzian rotation matrix, Rodrigues rotation formula
  • Akdeniz Üniversitesi Adresli: Evet

Özet

This study proposes a new way to represent elliptic and hyperbolic motions on any general hyperboloids of one or two sheets using the famous Rodrigues, Cayley, and Householder transformations. These transformations are used within the generalized Minkowski 3-space which extends the usual Lorentzian geometry by introducing a generalized scalar product. The study is carried out by considering the unit sphere defined in this generalized space along with the use of three-dimensional generalized Lorentzian skew-symmetric matrices that naturally generate continuous rotational motions. The obtained results provide rotational motions on the sphere in Minkowski 3-space as well as elliptic and hyperbolic motions on general hyperboloids in Euclidean 3-space. A numerical example is provided for each of the explored rotation methods.