Inverse problem and Bertrand's theorem
Mathematical Physics
2016-08-16 v1 General Mathematics
math.MP
Abstract
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.
Cite
@article{arxiv.math-ph/0612009,
title = {Inverse problem and Bertrand's theorem},
author = {Yves Grandati and Alain Bérard and Ferhat Menas},
journal= {arXiv preprint arXiv:math-ph/0612009},
year = {2016}
}
Comments
11 pages, 3 figures