Uso de las transformaciones de Lie para la determinación de órbitas periódicas simples
Abstract
A Hamiltonian system formed by an integrable part plus a small perturbation is considered. The goal of this work is to obtain a certain type of periodic orbits for it through the analysis of the normalized system. In fact, under some regularity conditions, the equilibria corresponding to the normal form are related to simple periodic orbits of the departure system. As a first step, the normalized Hamiltonian is calculated up to an adequate order of approximation, via Lie transformations, obtaining the symplectic change of variables consequently. Then, the inverse change of variables is calculated using again Lie transformations. In this way, the critical points of the normalized system are transformed so as to have approximated analytical conditions to generate periodic orbits of the original problem. These analytical conditions are the starting points to make numerical continuations of periodic orbits. We illustrate the approach with the calculation of periodic orbits of a system, which is an extension to three dimensions of the classical Hénon and Heiles problem in Galactic Dynamics.
- Publication:
-
Boletin de la Asociacion Argentina de Astronomia La Plata Argentina
- Pub Date:
- 1998
- Bibcode:
- 1998BAAA...42....5Y