A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-08-06 DOI:10.1002/mma.70020

Gül Tuğ, Zehra Özdemir

引用次数: 0

Abstract

In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.

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一种利用双曲运动学求解曲面增长的新方法

在目前的工作中，我们引入了利用双曲几何的表面增生。首先，我们沿着生成曲线描述双曲运动学，以构造具有双曲截面的增积曲面。得到的表面不仅具有双曲截面，而且其质点在形成过程中也遵循双曲轨迹。此外，我们通过使用双曲分割四元数作为另一种视角来解释这个过程。这表明上述表面的构造非常简单。然后，我们研究了这种曲面的速度和偏心率之间的关系，并与圆周运动进行了比较。我们在一种编程语言的帮助下给出了几个例子的可视化来支持理论结果。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.