Geodesic
Symmetries and stability of motions in the Newtonian and the Hookean potentials
Theoretical and applied mechanics, Tome 49 (2022) no. 1.

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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 
@article{TAM_2022_49_1_a4,
     author = {Christian Carimalo},
     title = {Symmetries and stability of motions in the {Newtonian} and the {Hookean} potentials},
     journal = {Theoretical and applied mechanics},
     pages = {61 - 69},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2022},
     url = {http://geodesic.mathdoc.fr/item/TAM_2022_49_1_a4/}
}
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Christian Carimalo. Symmetries and stability of motions in the Newtonian and the Hookean potentials. Theoretical and applied mechanics, Tome 49 (2022) no. 1. http://geodesic.mathdoc.fr/item/TAM_2022_49_1_a4/