Numerical Solution of Differential Equations of Elastic Curves in ۳-dimensional Anti-de Sitter Space

In this paper, we aim to extend the Darboux frame field into ۳-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_{۳} (i.e. ۳-dimensional Anti-de Sitter space). In this study, we investigate the elastic curves in AdS_{۳} and obtain equations through which elastic curves are found out. Therefore, we solve these equations numerically and finally plot and design some elastic curves.

کلیدواژه ها:

Darboux frame ، Elastic curve ، Geodesic curvature ، Anti-de Sitter space ، Euler-Lagrange equations