This article is cited in 1 paper

Transmutation of central forces and Bertrand's theorem

Christian Carimalo

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

Abstract: 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.

Keywords: classical mechanics, Bertrand's theorem.

MSC: 70F05, 70F15, 37N05

Received: 02.06.2022
Accepted: 19.12.2022

Language: English

DOI: 10.2298/TAM220602001C