Elliptical kinematics of the accretive surface growth

Authors

ZEHRA ÖZDEMİR
GÜL GÜNER

DOI

10.55730/1300-0098.3119

Abstract

The 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.

Keywords

Biomathematics, biological growth, Euclidean geometries, special curves, accretive growth, elliptical motions

First Page

728

Last Page

745

Recommended Citation

ÖZDEMİR, ZEHRA and GÜNER, GÜL (2022) "Elliptical kinematics of the accretive surface growth," Turkish Journal of Mathematics: Vol. 46: No. 3, Article 4. https://doi.org/10.55730/1300-0098.3119
Available at: https://journals.tubitak.gov.tr/math/vol46/iss3/4