On point-line displacement with elliptic screw motion

Uçak G. F., GÖK İ.

Journal of Mathematical Analysis and Applications, vol.552, no.2, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 552 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.1016/j.jmaa.2025.129787
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Elliptic dual Euler-Rodrigues formula, Elliptic dual quaternions, Elliptic screw, Point-line
  • Ankara University Affiliated: Yes

Abstract

The objective of this paper is to develop the concept of point-line displacement within the framework of elliptic space, denoted as Ra1,a2,a3. The study begins by summarizing the fundamental principles of elliptic dual quaternions and elliptic screw motion. Next, the notion of point-line displacement is rigorously defined in the context of elliptic inner product spaces, and its algebraic properties are thoroughly analyzed. Finally, the practical relevance of the proposed approach is demonstrated through an illustrative example that establishes the relationship between point-line geometry and the elliptic dual Euler-Rodrigues formula.