A Pedagogical Relook at Bertrand's Theorem

被引：1

作者：

Jeevitha, T. U. ^{[1
]}

Das, Sanjit ^{[2
]}

机构：

[1] VIT Chennai, Chennai, Tamil Nadu, India

[2] VIT Chennai, Sch Adv Sci, Chennai 600127, Tamil Nadu, India

来源：

RESONANCE-JOURNAL OF SCIENCE EDUCATION | 2019年 / 24卷 / 11期

关键词：

Closed bound orbits; Abel integral; Bertrand's theorem; central force; PROOF;

D O I：

10.1007/s12045-019-0892-3

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

Bertrand's theorem is one of the landmark results in the context of the central force problem in mechanics. It leads to the conditions for closed bound orbits. This pedagogical article intends to motivate the teacher as well as the student to engage in a formal proof of the theorem. We overview the basics of central forces and the Abel integral. Thereafter, we obtain the condition for closed orbits. We provide the reader with a broad panorama of areas/topics where Bertrand's theorem arises, including interesting scenarios in the regime of Einstein's general theory of relativity.

引用

页码：1235 / 1251

页数：17