Dual transformations and quaternions

YÜCA G., YAYLI Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.44, sa.14, ss.10957-10971, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 14
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/mma.7459
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.10957-10971
  • Anahtar Kelimeler: dual quaternion, dual transformation, kinematics, Lorentzian space, quaternion, rotation matrix, SURFACES, CURVES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, we are interested in the way quaternions to represent 3D and 4D rotations in Lorentzian space. We give a new method for obtaining a rotation matrix in Lorentzian space with the help of a unit quaternion. Furthermore, we prove that rotation matrices correspond to a quaternion leave invariant the same axis in Euclidean and Lorentzian space. Then, we introduce a semi-orthogonal matrix representation of a quaternion curve in 4D space. Moreover, we provide applications and draw their figures to explore visual representations. Finally, due to the importance of the dual space in kinematics, robotics, and other areas related, we carry this work into their dual spaces by using a dual quaternion.