Dual Split Quaternions and Chasles' Theorem in 3-Dimensional Minkowski Space

Ramis C., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.23, no.4, pp.951-964, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.1007/s00006-013-0405-5
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.951-964
  • Keywords: Chasles' theorem, Cayley's formula, screw motion, dual split quaternion, dual semi orthogonal matrix, SCREW MOTION
  • Ankara University Affiliated: Yes

Abstract

In 1831, Michel Chasles proved the existence of a fixed line under a general displacement in . The fixed line called the screw axis of displacement was obtained by McCharthy in [10]. The purpose of this paper is to develop the method which is given for the pure rotation in [14], and thus to obtain the screw axis of spatial displacement in 3-dimensional Minkowski space. Firstly, we give a relation between dual vectors and lines in , characterize the screw axis. Also, we discuss the dual split quaternion representation of a spatial displacement.