The determination of the apsidal angles and Bertrand's theorem

Details The determination of the apsidal angles and Bertrand's theorem The determination of the apsidal angles and Bertrand's theorem

2008-09-11

arxiv.org/abs/0809.2069v1

Physics

Classical Physics

Latex file, one figure; submitted for publication

Scientific paper

10.1103/PhysRevE.79.036605

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.

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