Dual octonions and rigid body kinematics


Çakır H., Bektaş Ö., Yılmaz R.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.0, no.0, pp.1-18, 2024 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 0 Issue: 0
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.9899
  • 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.1-18
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

In this paper, we first give the basic information about octonions and present the Euclidean rotation matrix formed by an octonion in seven‐dimensional Euclidean space. Next, we define and introduce the ‐module and dual vectors using dual numbers. Then, we provide the transformation that maps the points on the unit dual sphere one‐to‐one with the directed lines in . We also define a subset of the unit dual sphere, demonstrating that each element of this subset corresponds to two intersecting perpendicular directed lines in seven‐dimensional Euclidean space. Following that, we introduce dual octonions with their basic algebraic properties and examine rigid body (screw) motions in seven‐dimensional Euclidean space using dual octonions. Finally, we define an operator and express that this operator transforms two perpendicular intersecting directed lines in seven‐dimensional Euclidean space into two perpendicular intersecting directed lines.