A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics

TUĞ G., Özdemir Z.

Mathematical Methods in the Applied Sciences, vol.48, no.16, pp.15349-15363, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 16
  • Publication Date: 2025
  • Doi Number: 10.1002/mma.70020
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.15349-15363
  • Keywords: accretive growth, biological growth, biomathematics, Clifford algebra, Euclidean geometries, hyperbolical kinematics, special curves
  • Karadeniz Technical University Affiliated: Yes

Abstract

In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.