The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane
IF 2.6
2区 数学
Q1 MATHEMATICS, APPLIED
引用次数: 0
Abstract
In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is introduced. In both spaces, a catenary is defined as the shape of a hanging chain when its potential energy is determined by the distance to a given geodesic of the space. Several characterizations of the catenary are established in terms of the curvature of the curve and of the angle that its unit normal makes with a vector field of the ambient space. Furthermore, in the hyperbolic plane, we extend the concept of catenary substituting the reference geodesic by a horocycle or the hyperbolic distance by the horocycle distance.
球面和双曲面中的悬链问题
本文介绍了球面和双曲面中的导管曲线概念。在这两个空间中，当悬链的势能由到空间给定测地线的距离决定时，悬链被定义为悬链的形状。根据曲线的曲率及其单位法线与环境空间向量场的夹角，确定了悬链的几个特征。此外，在双曲面中，我们扩展了全缘的概念，用角环来代替参考大地线，或用角环距离来代替双曲距离。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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来源期刊
CiteScore
5.00
自引率
3.30%
发文量
87
审稿时长
4.5 months
期刊介绍：
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be.
All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.
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