Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

Keçilioǧlu O., Özkaldi S., Gündoǧan H.

Advances in Applied Clifford Algebras, vol.22, no.4, pp.1081-1091, 2012 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1007/s00006-011-0318-0
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1081-1091
  • Keywords: Lorentzian matrix multiplication, Lorentzian space, rotation, split quaternions
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In the present paper we obtain the timelike Euler parameters of a Lorentzian orthogonal matrix in Lorentz space L3 = ℝ2,1 by using Lorentzian matrix multiplication. Then, by using the timelike Euler parameters of a given rotation in a split quaternion formulation, we produce split quaternion equation of a rotation motion in L3. Moreover the components of a dual split quaternion are obtained by replacing the timelike L-Euler parameters with their split dual versions. © 2011 Springer Basel AG.