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/