Determination of the apsidal angles and Bertrand's theorem.
We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. This formula can be useful in the calculation of precession rates. Then we discuss under what conditions the apsidal angles remain independent of the mechanical energy and angular momentum in the central force problem and, as a consequence, an alternative and nonperturbative proof of Bertrand's theorem is obtained.
Santos
Filadelfo C
FC
Instituto de Física, Universidade Federal do Rio de Janeiro, Cidade Universitária, P.O. Box 21945-970, Rio de Janeiro, Brazil. filadelf@if.ufrj.br
Soares
Vitorvani
V
Tort
Alexandre C
AC