APPLICATIONS OF QUATERNIONS IN GALILEAN SPACES

YÜCA G., YAYLI Y.

JOURNAL OF SCIENCE AND ARTS, sa.1, ss.133-148, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2022
  • Doi Numarası: 10.46939/j.sci.arts-22.1-a12
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.133-148
  • Anahtar Kelimeler: quaternion, dual quaternion, dual transformation, Galilean space, pseudo-Galilean space, KINEMATICS, SURFACES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, Galilean orthogonal matrices in G(5) and G(1)(5) are obtained with the help of unit quaternions. Moreover, Galilean orthogonal matrices in G(4) and G(1)(4) are acquired. These matrices produce Galilelan motions in Galilean spaces. We investigate the invariance of the plane where shear motion is acting in Galilean and pseudo-Galilean spaces. Additionally, related examples of matrices that belong to both spaces are provided. With a similar method, dual Galilean orthogonal matrices are obtained by using unit dual quaternions. Finally, we strengthen our work with examples and draw their figures to explore visual representations.