自由落体的数学分析

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2024-07-02 DOI:10.1007/s13160-024-00662-6

Tetsuya Kazumi, Shinsuke Nishikawa

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引用次数: 0

摘要

如果将悬挂在半空中的弹弓从最初的静止位置松开，你会发现一个有趣的现象：弹弓的底部会在半空中静止一段时间。在物理学家中，这一现象已广为人知，并已从物理角度进行了讨论。在本文中，我们从纯数学的角度探讨了自由下落的弹弓问题。通过严格的数学计算过程，我们得到了一个描述自由落体运动的明确公式，并证明这是一个不均匀波方程的解。我们的工作为物理学家获得的结果提供了数学上的依据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Mathematical analysis of a freely falling slinky

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Mathematical analysis of a freely falling slinky

If you release a slinky hung in midair from its initial stationary position, you can observe something interesting: the bottom of the slinky is at rest in midair for a while. Among physicists, this phenomenon is well known and has been discussed from the physical point of view. In this paper we deal with the problem of a freely falling slinky from the purely mathematical point of view. Through the rigorous mathematical process we obtained an explicit formula which describes the motion of the freely falling slinky and it turns out that this is a solution to an inhomogeneous wave equation. Our work gives the mathematical justification of the results obtained by physicists.

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.