Generalization of the catenary in the dual plane
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911479462100992 |
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| author | Aydin, Muhittin Evren López, Rafael |
| author_facet | Aydin, Muhittin Evren López, Rafael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalization of the catenary in the dual plane Aydin, Muhittin Evren López, Rafael Differential Geometry 53A04, 53A17, 53C42 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. |
| title | Generalization of the catenary in the dual plane |
| topic | Differential Geometry 53A04, 53A17, 53C42 |
| url | https://arxiv.org/abs/2603.02107 |