On the numerical continuation of periodic orbits

An intrinsic, 3-dimensional, differential, predictor-corrector algorithm

¹ Real Instituto y Observatorio de la Armada, 11110 San Fernando, Spain
² Escuela Técnica Superior de Ingenieros Aeronáuticos. Universidad Politécnica, 28040 Madrid, Spain

Corresponding author: M. Lara, mlara@roa.es

Received: 17 January 2000
Accepted: 25 March 2002

Abstract

This paper deals with the analytic continuation of periodic orbits of conservative dynamical systems with three degrees of freedom. For variations of any parameter (or integral), it relies on numerical analysis in order to implement a predictor-corrector algorithm to compute the initial conditions of the periodic orbits pertaining to the family. The method proposed here is not restricted to symmetric problems and, since the procedure involves the computation of the variational equations, a side effect is the trivial computation of the linear stability of the periodic orbits. As an illustration of the robustness of the method, several families of periodic orbits of the Restricted Three-Body Problem are computed.