Dual octonions and rigid body kinematics
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.47, no.7, pp.5957-5974, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 47 Issue: 7
- 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.5957-5974
- Keywords: dual octonions, kinematics, octonions, screw motion
- 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 𝔻�7-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 Double-struck capital R7$$ {\mathrm{\mathbb{R}}} circumflex 7 $$. 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.