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Theoretical and Applied Mechanics, 2022, Volume 49, Issue 1, Pages 61–69
DOI: https://doi.org/10.2298/TAM220213005C (Mi tam113) 		 
Symmetries and stability of motions in the Newtonian and the Hookean potentials

Christian Carimalo

Campus Pierre et Marie Curie, Sorbonne Université, Paris, France
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DOI: https://doi.org/10.2298/TAM220213005C
Abstract: A new way of looking at symmetries is proposed, especially regarding their role in the stability of two-body motions in the Newtonian and the Hookean potentials, the two selected by Bertrand's theorem. The role of the number of spatial dimensions is also addressed.
Keywords: classical mechanics, dynamical symmetry, Bertrand's theorem, Kepler problem.
Received: 13.02.2022
Document Type: Article
MSC: Primary 70G65; Secondary 70F05
Language: English
Citation: Christian Carimalo, “Symmetries and stability of motions in the Newtonian and the Hookean potentials”, Theor. Appl. Mech., 49:1 (2022), 61–69
Citation in format AMSBIB
\Bibitem{Car22}
\by Christian~Carimalo
\paper Symmetries and stability of motions in the Newtonian and the Hookean potentials
\jour Theor. Appl. Mech.
\yr 2022
\vol 49
\issue 1
\pages 61--69
\mathnet{http://mi.mathnet.ru/tam113}
\crossref{https://doi.org/10.2298/TAM220213005C}
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