Inverse problem and Bertrand's theorem

Details Inverse problem and Bertrand's theorem Inverse problem and Bertrand's theorem

2006-12-03

arxiv.org/abs/math-ph/0612009v1

Am.J.Phys.76:782-787,2008

Physics

Mathematical Physics

11 pages, 3 figures

Scientific paper

10.1119/1.2899733

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.

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