The geometrical and algebraic interpretations of Euler-Rodrigues formula in Minkowski 3-space

Kahveci D., YAYLI Y., GÖK İ.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, sa.10, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0219887816501164
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Euler-Rodrigues formula, split quaternions, Lorentzian Lie groups, Lorentzian Lie algebras, DUAL SPLIT QUATERNIONS, ROTATIONS, SPACE
  • Ankara Üniversitesi Adresli: Evet

Özet

The aim of this paper is to give the geometrical and algebraic interpretations of Euler-Rodrigues formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in R-3(1) and angle, the spatial displacement is represented by a 3x3 semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler-Rodrigues formula in terms of semi-skew-symmetric matrix corresponds to space-like, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler-Rodrigues formula is expressed via split quaternions in Minkowski 3-space.