Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space

Abstract

In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive differential equations for non-null elastic curves in AdS$_{3}$ (i.e. 3-dimensional Anti-de Sitter space). In this study, we investigate the elastic curves in AdS$_{3}$ and obtain equations through which elastic curves are found out. Therefore, we solve these equations numerically and finally plot and design some elastic curves.

Keywords

• darboux frame
• elastic curve
• geodesic curvature
• anti-de sitter space
• euler-lagrange equations