Study on the Problem of “Catenary Pendulum”

HomePage >> Journals >> Mathematical Computation

Mathematical Computation

Mathematical Computation is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology, economy... [More] Mathematical Computation is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology, economy and science, report of latest research result, aiming at providing a good communication platform to transfer, share and discuss the theoretical and technical development of mathematics theory development for professionals, scholars and researchers in this field, reflecting the academic front level, promote academic change and foster the rapid expansion of mathematics theory and application technology.

The journal receives manuscripts written in Chinese or English. As for Chinese papers, the following items in English are indispensible parts of the paper: paper title, author(s), author(s)'affiliation(s), abstract and keywords. If this is the first time you contribute an article to the journal, please format your manuscript as per the sample paper and then submit it into the online submission system. Accepted papers will immediately appear online followed by printed hard copies by Ivy Publisher globally. Therefore, the contributions should not be related to secret. The author takes sole responsibility for his views.

ISSN Print:2327-0519

ISSN Online:2327-0527

Email:mc@ivypub.org

Website: http://www.ivypub.org/mc/

		0
		0

Navigation

News

All articles submitted to this journal are required to be tested by AMLC.

This journal is full-text indexed by CNKI which is the China's most authoritative academic resources database.

This journal is full-text indexed by Open J-Gate.

Paper Infomation

Study on the Problem of “Catenary Pendulum”

Full Text(PDF, 2073KB)

Author: Changrun Zhao

Abstract: The study of the “catenary pendulum” problem reveals intrinsic connections between the catenary curve and the brachistochrone (cycloid), leading to three key conclusions: (i) Among pendulums of equal length—the catenary pendulum, simple pendulum, and compound pendulum—the catenary pendulum exhibits the shortest oscillation period. (ii) The motion of the system's center of mass forms a brachistochrone curve, which constitutes the fundamental dynamic characteristic of the catenary pendulum. Notably, the midpoint of the rope has a significantly smaller amplitude than the system's center of mass. (iii) The free end of the catenary pendulum (its terminal point) represents the most dynamically active particle. Its trajectory forms an arc-shaped elliptical orbit symmetric with respect to the y-axis.

Keywords: Catenary Pendulum; Catenary; Optimal Sag; Cycloid; Rolling Circle's Initial Contact Angle

References:

[1] 周衍柏.理论力学.高等教育出版社， 1985.125-128

[2] 郭大钧.大学数学手册.山东科学技术出版社，1985.487-487

[3] 周培源.理论力学.人民教育出版社，1952.287-289

[4] 华罗庚.高等数学引论(第二分册).科学出版，1963.13-14

[5] B.И.斯米尔诺夫著孙念增译，高等数学教程（第一卷）.人民教育出版社， 1979.180-183

[6] 赵凯华.定性与半定量物理学.高等教育出版社，1991.1-6

[7] 赵长润.椭圆周长的初等公式.数学计算(中英文版)，2023, 11(2): 7-20.