Dual octonions representation of rigid body motions
20th International Geometry Symposium. In Honor of Prof. Dr. H. Hilmi Hacısalihoğlu, Van, Turkey, 18 - 20 July 2024, pp.82, (Summary Text)
- Publication Type: Conference Paper / Summary Text
- City: Van
- Country: Turkey
- Page Numbers: pp.82
- Recep Tayyip Erdoğan University Affiliated: Yes
Abstract
In this paper, we first provide fundamental information about octonions and present the Euclidean rotation matrix generated by an octonion in 7-dimensional Euclidean space. Subsequently, we define and
introduce the D7 module and dual vectors using dual numbers. Following this, we establish a transformation that bijectively maps points
on the unit dual sphere to directed lines in R7
. Additionally, we define
a subset of the unit dual sphere and demonstrate that each element
of this subset corresponds to two intersecting orthogonal angles. We
then focus on directed lines in 7-dimensional Euclidean space. In the
subsequent section, we introduce the basic algebraic properties of dual
octonions and investigate rigid body (screw) motions in 7-dimensional
Euclidean space using these octonions. Finally, we define an operator
that transforms two intersecting orthogonal lines into two intersecting
orthogonal segments in 7-dimensional Euclidean space.