Dual octonions representation of rigid body motions

Çakır H., Bektaş Ö., Yılmaz R.

20th International Geometry Symposium. In Honor of Prof. Dr. H. Hilmi Hacısalihoğlu, Van, Türkiye, 18 - 20 Temmuz 2024, ss.82

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Van
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.82
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.