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A Pedagogical Relook at Bertrand’s Theorem
T. U J,
Published in Springer Science and Business Media LLC
Volume: 24
Issue: 11
Pages: 1235 - 1251
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. © 2019, Indian Academy of Sciences.
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