The determination of the apsidal angles and Bertrand's theorem
Classical Physics
2013-04-18 v1 General Physics
Abstract
We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. Then we discuss under what conditions the apsidal angles remain independent of the mechanical energy and angular momentum in the central force problem. As a consequence, an alternative and non-perturbative proof of Bertrand's theorem is obtained.
Cite
@article{arxiv.0809.2069,
title = {The determination of the apsidal angles and Bertrand's theorem},
author = {Filadelfo C. Santos and Vitorvani Soares and Alexandre C. Tort},
journal= {arXiv preprint arXiv:0809.2069},
year = {2013}
}
Comments
Latex file, one figure; submitted for publication