Curves whose pseudo spherical indicatrices are elastic
Turkish Journal of Mathematics, vol.42, no.6, pp.3123-3132, 2018 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 42 Issue: 6
- Publication Date: 2018
- Doi Number: 10.3906/mat-1801-44
- Journal Name: Turkish Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.3123-3132
- Keywords: Elastic curve, Euler-Lagrange equation, Pseudo spherical indicatrix
- Isparta University of Applied Sciences Affiliated: Yes
Abstract
The pseudo spherical indicatrix of a curve in Minkowski 3-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter 2-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski 3-space. Then we give some results of solutions of these equations.