Affiliation:
1. Campus Pierre et Marie Curie, Sorbonne Université, Paris, France
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.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Mechanical Engineering,Computational Mechanics
Reference19 articles.
1. J. Bertrand, Théorème relatif au mouvement d’un point attiré vers un centre fixe, C. R. Acad. Sci., Paris 77(16) (1873), 849-853.
2. C. Carimalo, Dynamical symmetries behind Bertrand’s theorem, Am. J. Phys. 89 (2021), 1012, DOI: 10.1119/10.0005452.
3. R.P. Martinez-y-Romero, H. N. Múñez-Yépez, A. L. Salas-Brito, Periodic orbits, superintegrability, and Bertrand’s theorem, AIP Advances 10 (2020), 065003, DOI: 10.1063/1.5143582.
4. P. S. Laplace, Traité de Mécanique Céleste, Tome I, Première partie, Livre II, 1799, 165.
5. C. Runge, Vektoranalysis, Leipzig, 1919.