Dual transformations and quaternions

YÜCA G., YAYLI Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.14, pp.10957-10971, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 14
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7459
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: 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
  • Page Numbers: pp.10957-10971
  • Keywords: dual quaternion, dual transformation, kinematics, Lorentzian space, quaternion, rotation matrix, SURFACES, CURVES
  • Ankara University Affiliated: Yes

Abstract

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.