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ЖУРНАЛЫ // Theoretical and Applied Mechanics // Архив

Theor. Appl. Mech., 2023, том 50, выпуск 1, страницы 1–11 (Mi tam122)

Эта публикация цитируется в 1 статье

Transmutation of central forces and Bertrand's theorem

Christian Carimalo

Sorbonne Université, Campus Pierre et Marie Curie, Paris, France

Аннотация: The transmutation of central forces, or dual law, is a transformation linking potentials in power law relative to the distance, that is, those having a positive exponent to those having a negative exponent. A well known example is that of the Newtonian and Hookean potentials, which are also strongly linked by Bertrand's famous theorem. This article shows how the use of dual law provides a better understanding of this theorem, and a new way to complete its demonstration.

Ключевые слова: classical mechanics, Bertrand's theorem.

MSC: 70F05, 70F15, 37N05

Поступила в редакцию: 02.06.2022
Принята в печать: 19.12.2022

Язык публикации: английский

DOI: 10.2298/TAM220602001C



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