Dynamics in the center manifold of the collinear points of the restricted three body problem

Physica D: Nonlinear Phenomena

Volumn 132, Issue 1-2, 1999, Pages 189-213

  Jorba, Àngel ^a   Masdemont, Josep ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

02.30.Hq; 02.40.Vh; 02.60. x; 95.10.Ce; Center manifolds; Halo orbits; Lissajous orbits; Lower dimensional tori; Normally hyperbolic manifolds

Indexed keywords

EID: 0000379181     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00042-1     Document Type: Article

References (26)

1. V. Szebehely, Theory of Orbits, Academic Press, New York, 1967.
2. Eliasson L.H. Perturbations of stable invariant tori for Hamiltonian systems. Ann. Sc. Norm. Super. Pisa Cl. Sci. Ser. IV. 15(1):1988;115-147.
3. Jorba À., Villanueva J. On the normal behaviour of partially elliptic lower dimensional tori of Hamiltonian systems. Nonlinearity. 10:1997;783-822.
4. H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars (1892, 1893, 1899).
5. Farquhar R.W Halo-orbit and Lunar-Swingby missions of the 1990's. Acta Astronautica. 24:1991;227-234.
6. R.W. Farquhar, D.P. Muhonen, C. Newman, H. Heuberger, The first libration point satellite. Mission overview and flight history, AAS/AIAA Astrodynamics Spec. Conf., 1979.
7. K.C. Howell, B.T. Barden, R.S. Wilson, M.W. Lo, Trajectory Design Using a Dynamical Systems Approach with Application to Genesis, AAS Paper 97-709. AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, Idaho, 1997.
8. Howell K.C., Pernicka H.J. Numerical determination of Lissajous trajectories in the restricted three-body problem. Celestial Mechanics. 41:1988;107-124.
9. Huber M.C.E. The history of the SOHO mission. ESA Bulletin. 86:1996;25-35.
10. Richardson D.L. Halo orbit formulation for the ISEE-3 mission. J. Guidance and Control. 3:1980;543-548.
11. G. Gómez, À. Jorba, J. Masdemont, C. Simó, Study Refinement of Semi-Analytical Halo Orbit Theory, ESOC Contract 8625/89/D/MD(SC), Final Report, 1991.
12. G. Gómez, J. Masdemont, C. Simó, Quasihalo orbits associated with libration points, to appear in Journal of the Astronautical Sciences.
13. Jorba À., Villanueva J. On the persistence of lower dimensional invariant tori under quasi-periodic perturbations. J. Nonlinear Science. 7:1997;427-473.
14. À. Jorba, A methodology for the numerical computation of normal forms, centre manifolds and first integrals of hamiltonian systems, to appear in Exp. Math., 1999.
15. À. Jorba, J. Masdemont, Nonlinear dynamics in an extended neigbourhood of the translunar libration point, in: Hamiltonian Systems with Three or More Degrees of Freedom, C. Simó (Ed.), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. Kluwer, Dordrecht, Holland (to appear).
16. C. Simó, Effective computations in celestial mechanics and astrodynamics, lectures given at CISM Course on Modern Methods of Analytical Mechanics and their Applications, Udine, Italy, 1997.
17. J. Cobos, C. Simó, Reduction to the Central Manifold around a Collinear Libration Point of the Restricted Three Body Problem, Proceedings of the XV CEDYA / V CMA, 1998, pp. 673-676.
18. G. Gómez, J. Llibre, R. Martinez, C. Simó, Station Keeping of Libration Point Orbits, ESOC Contract 5684/83/D/JS(SC), Final Report, 1985.
19. Richardson D.L. A Note on a Lagrangian Formulation for Motion about the Collinear Points. Celestial Mechanics. 22:1980;231-236.
20. Giorgilli A., Delshams A., Fontich E., Galgani L., Simó C. Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem. J. Diff. Eq. 77:1989;167-198.
21. À. Jorba, R. Llave, Regularity properties of center manifolds and applications, in preparation.
22. Bazzani A., Giovannozzi G., Servizi G., Todesco E., Turchetti G. Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps. Physica D. 64:1993;66-97.
23. Benettin G., Giorgilli A. On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms. J. Stat. Phys. 74:1994;1117-1143.
24. Deprit A. Canonical transformations depending on a small parameter. Cel. Mech. 1:1969;12-30.
25. Gómez G., Masdemont J., Simó C. Lissajous orbits around Halo orbits. Advances in the Astronautical Sciences. 95:1997;117-134.
26. Jorba À., Villanueva J. Numerical computation of normal forms around some periodic orbits of the restricted three body problem. Physica D. 114:1998;197-229.