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- Title
Dual octonions and rigid body kinematics.
- Authors
Çakır, Hasan; Bektaş, Özcan; Yılmaz, Ruşen
- 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 D7-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 R7. 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.
- Subjects
CAYLEY numbers (Algebra); KINEMATICS
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 7, p5957
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9899