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Zbl 1214.70002
Lara, M.; Peláez, J.
On the numerical continuation of periodic orbits. An intrinsic, 3-dimensional, differential, predictor-corrector algorithm. (English)
[J] Astron. Astrophys. 389, No. 2, 692-701 (2002). ISSN 0004-6361; ISSN 1432-0746/e

Summary: 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), we use a predictor-corrector algorithm to compute the initial conditions for periodic orbits pertaining to the family. The method proposed here is not restricted to symmetric problems and, since the procedure involves the computation of variational equations, a side effect is the trivial computation of the linear stability of periodic orbits. As an illustration of the robustness of the method, we compute several families of periodic orbits of the restricted three-body problem.

MSC 2000:: *70-08 Computational methods (mechanics of particles and systems)
70F07 Three-body problem
70F15 Celestial mechanics

Keywords: variational equations; linear stability; restricted three-body problem

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