Generalization of the catenary in the dual plane
Abstract
In this paper, we study a dual analogue of the classical catenary within the class of admissible curves in the dual plane $\mathbb{D}^2$. We introduce $α$-catenaries in $\mathbb{D}^2$ as stationary points of a potential energy functional, where $α\in \mathbb{R}$ is a real parameter. We derive the corresponding Euler-Lagrange equations and obtain explicit equations of these curves for specific values of $α$. Furthermore, we establish a geometric characterization of $α$-catenaries in terms of their curvature and unit normal vector field.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Mathematics and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 March 2026
- Language
- EN
- Document type
- Preprint