Generalized Galilean Rotations

Creative Commons License

ÇOLAKOĞLU H. B., Öztürk İ., Çelik O., ÖZDEMİR M.

Symmetry, cilt.16, sa.11, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 11
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/sym16111553
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Cayley map, Galilean transformation, generalized scalar product, Householder map, Rodrigues formula, rotation matrix
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this article, we give rotational motions on any straight line or any parabola in a scalar product space. To achieve this goal, we first define the generalized Galilean scalar product and determine the generalized Galilean skew symmetric and orthogonal matrices. Then, using the well-known Rodrigues, Cayley, and Householder maps, we produce the generalized Galilean rotation matrices. Finally, we show that these rotation matrices can also be used to determine parabolic rotational motion.