Generalized Galilean Rotations

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

Symmetry, vol.16, no.11, 2024 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 16 Issue: 11
  • Publication Date: 2024
  • Doi Number: 10.3390/sym16111553
  • Journal Name: Symmetry
  • Journal Indexes: 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
  • Keywords: Cayley map, Galilean transformation, generalized scalar product, Householder map, Rodrigues formula, rotation matrix
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

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.