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

Ramis C., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.23, sa.4, ss.951-964, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s00006-013-0405-5
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.951-964
  • Anahtar Kelimeler: Chasles' theorem, Cayley's formula, screw motion, dual split quaternion, dual semi orthogonal matrix, SCREW MOTION
  • Ankara Üniversitesi Adresli: Evet

Özet

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.