Elliptical kinematics of the accretive surface growth

Özdemİr Z., TUĞ G.

Turkish Journal of Mathematics, cilt.46, sa.3, ss.728-745, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3906/mat-2102-76
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.728-745
  • Anahtar Kelimeler: Biomathematics, biological growth, Euclidean geometries, special curves, accretive growth, elliptical motions, CLASSICAL SEASHELL PROBLEM, FORMULATION
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

© This work is licensed under a Creative Commons Attribution 4.0 International LicenseThe stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of surface. Thus, we introduce the elliptical kinematics along an initial curve and construct some accretive surfaces with an elliptical cross-section. In fact, these surfaces are not only curves with an elliptical cross-sectional curve, but also the material points of the surface follow an elliptical trajectory during their formation. This situation can be easily explained through elliptical motion and elliptical quaternion algebra. Then, we investigate the relationship between velocity and eccentricity of the surfaces and compare it to the case of circular motion. Furthermore, we visualize some examples to support the theoretical results through the MAPLE program