A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.48, sa.16, ss.15349-15363, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 48 Sayı: 16
- Basım Tarihi: 2025
- Doi Numarası: 10.1002/mma.70020
- Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
- Sayfa Sayıları: ss.15349-15363
- Ankara Üniversitesi Adresli: Hayır
Özet
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.