Hyper-dual split quaternions and rigid body motion

Aslan S., BEKAR M., YAYLI Y.

JOURNAL OF GEOMETRY AND PHYSICS, cilt.158, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 158
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.geomphys.2020.103876
  • Dergi Adı: JOURNAL OF GEOMETRY AND PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Hyper-dual numbers, Hyper-dual split vectors, Hyper-dual split quaternions, ROTATIONS, NUMBERS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce and define hyper-dual split vectors by using hyper-dual numbers. We define three subsets; two of them are subsets of Lorentzian unit hyper-dual sphere and the other is a subset of hyperbolic unit hyper-dual sphere. We show that to each element of these subsets corresponds two intersecting perpendicular lines in Minkowski space. We also introduce and define hyper-dual split quaternions with their basic algebraic properties. We give the geometric interpretation of hyper-dual split quaternions, and we define three new operators in Minkowski space. We show that these operators turn each two intersecting perpendicular lines again to two intersecting perpendicular lines in Minkowski space. Examples are also provided to illustrate our theorems and results. (C) 2020 Elsevier B.V. All rights reserved.