Geodesic
Transmutation of central forces and Bertrand's theorem
Theoretical and applied mechanics, Tome 50 (2023) no. 1

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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Christian Carimalo. Transmutation of central forces and Bertrand's theorem. Theoretical and applied mechanics, Tome 50 (2023) no. 1. http://geodesic.mathdoc.fr/item/TAM_2023_50_1_a1/