Quasihalo orbits associated with libration points

Journal of the Astronautical Sciences

Volumn 46, Issue 2, 1998, Pages 135-176

  Gomez G ^a   Masdemont, J ^b   Simo C ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NUMERICAL ANALYSIS; SOLAR SYSTEM;

LIBRATION POINTS; LINDSTEDT-POINCARE METHOD; QUASIHALO ORBITS;

ORBITS; ORBITAL TRANSFER;

ANALYSIS / DESIGN; CIRCULAR RESTRICTED THREE-BODY PROBLEMS; COLLINEAR LIBRATION POINTS; EXCLUSION ZONES; HALO ORBITS; JET PROPULSION LABORATORY; LIBRATION POINT; SEMI-ANALYTICAL;

EID: 0032277757     PISSN: 00219142     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. GOUDAS, C. L. "Three Dimensional Periodic Orbits and their Stability," Icarus, Vol. 2, 1963, pp. 1-18.
2. HÉNON, M. "Vertical Stability of Periodic Orbits in the Restricted Problem I. Equal Masses," Astronomy & Astrophysics, Vol. 28, 1973, pp. 415-426.
3. ZAGOURAS, C. G., and KAZANTZIS, P. G. "Three-Dimensional Periodic Oscillations Generating from Plane Periodic Ones Around the Collinear Lagrangian Points," Astrophysics Space Science, Vol. 61, 1979, pp. 389-409.
4. RICHARDSON, D. L. "Analytical Constructions of Periodic Orbits about the Collinear Points," Celestial Mechanics, Vol. 22, 1980, pp. 241-253.
5. FARQUHAR, R. W. "Halo-Orbit and Lunar-Swingby Missions of the 1990's," Acta Astronautica Vol. 24, 1991, pp. 227-234.
6. FARQUHAR, R. W., and KAMEL, A. A. "Quasi-Periodic Orbits about the Translunar Libration Point," Celestial Mechanics, Vol. 7, 1973, pp. 458-473.
7. HOWELL, K.C., and PERNICKA, H.J. "Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem," Celestial Mechanics, Vol. 41, 1988, pp. 107-124.
8. RICHARDSON, D. L., and CARY, N. D. "A Uniformly Valid Solution for Motion About the Interior Libration Point of the Perturbed Elliptic-Restricted Problem," Paper No. 75-021, AAS/AIAA Astrodynamics Specialist Conference, Nassau, Bahamas, July 1975.
9. SHARER, P., ZSOLDOS, J., and FOLTA, D. "Control of Libration Point Orbits Using Lunar Gravity-Assisted Transfer," Advances in the Astronomical Sciences, Vol. 84, 1993, pp. 651-663.
10. GÓMEZ, G., JORBA, À., MASDEMONT, J., and SIMÓ, C. "Study Refinement of Semi-Analytical Halo Orbit Theory," ESOC Contract 8625/89/D/MD(SC), Final Report, Barcelona, April 1991.
11. GÓMEZ, G., MASDEMONT, J., and SIMO, C. "Lissajous Orbits Around Halo Orbits," Advances in the Astronautical Sciences, Vol. 95, 1997, pp. 117-134.
12. JORBA, À., and MASDEMONT, J. "Nonlinear Dynamics in an Extended Neighborhood of the Translunar Equilibrium Point," NATO-ASI Hamilton Systems with Three or More Degrees of Freedom, C. Simó (editor), 1999, Kluwer (in press).
13. JORBA, À., and VILLANUEVA, J. "On the Normal Behavior of Partially Elliptic Lower Dimensional Tori of Hamilton Systems," Nonlinearity, Vol. 10, 1997, pp. 783-822.
14. JORBA, À, and VILLANUEVA, J. "Numerical Computation of Normal Forms Around Some Periodic Orbits of the Restricted Three Body Problem," Physica D, Vol. 114, 1998, pp. 197-229.
15. RICHARDSON, D. L. "A Note on the Lagrangian Formulation for Motion About the Collinear Points," Celestial Mechanics, Vol. 22, 1980, pp. 231-236.
16. GÓMEZ, G., LLIBRE, J., MARTINEZ, R., and SIMÓ, C. "Station Keeping of Libration Point Orbits," ESOC Contract 5648/83/D/JS(SC), Final Report, Barcelona, November 1985.
17. GIACAGLIA, G. E. O. Perturbation Methods in Non-Linear Systems, Springer-Verlag, 1972.
18. POINCARÉ, H. Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars, 1892, 1893, 1899.
19. JORBA, À., and SIMÓ, C. "On Quasiperiodic Perturbations of Elliptic Equilibrium Points," SIAM Journal of Mathematical Analysis, Vol. 27, 1996, pp. 1704-1737.
20. JORBA, À., and VILLANUEVA, J. "On the Persistence of Lower Dimensional Invariant Tori Under Quasiperiodic Perturbations," Journal of Nonlinear Science, Vol. 7, 1997, pp. 427-473.
21. FARQUHAR, R.W., MUHONEN, O.P., NEWMAN, C, and HEUBERGER, H. "The First Libration Point Satellite. Mission Overview and Flight History," AAS/AIAA Astrodynamics Specialist Conference, 1979.
22. GÓMEZ, G., JORBA, À., MASDEMONT, J., and SIMÓ, C. "Moon's Influence on the Transfer from the Earth to a Halo Orbit," Predictability, Stability and Chaos in N-Body Dynamical System, A. Roy (editor). Plenum Press, 1991, pp. 283-290.
23. GÓMEZ, G., JORBA, À., MASDEMONT, J., and SIMÓ, C. "A Dynamical Systems Approach for the Analysis of the SOHO Mission," Proceedings of the Third International Symposium on Spacecraft Flight Dynamics. ESA SP-326, 1991, pp. 449-454.
24. 1," Celestial Mechanics, Vol. 56, 1993, pp. 541-562.
25. HUBER, M. C. E., BONNET, R. M., DALE, D.C., AROUINI, M., FROMLICH, C., DOMINGO, V., and WHITCOMB, G. "The History of the SOHO Mission," ESA Bulletin, Vol. 86, 1996, pp. 25-35.
26. RICHARDSON, D. L. "Halo Orbit Formulation for the ISEE-3 Mission," Journal of Guidance and Control, Vol. 3, 1980, pp. 543-548.
27. RODRÍGUEZ-CANABAL, J. "Operational Halo Orbit Maintenance Technique for SOHO," Second International Symposium on Spacecraft Flight Dynamics, ESA SP-255, 1986, pp. 71-78.
28. HOWELL, K. C., BARDEN, B.T., WILSON, R. S., and LO, M. W. "Trajectory Design Using a Dynamical Systems Approach with Application to Genesis," Paper No. 97-709, AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, Idaho, August 1997.
29. CODDINGTON, E. A., and LEVINSON, N. Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
30. BREAKWELL, J. V., KAMEL, A. A., and RATNER, M. J. "Station-Keeping for a Translunar Communications Station," Celestial Mechanics, Vol. 10, 1974, pp. 357-373.
31. HOWELL, K. C., and PERNICKA, H. J. "Station-Keeping Method for Libration Point Trajectories," Journal of Guidance, Control, and Dynamics, Vol. 6, 1980, pp. 549-554.
32. 1 Libration Point Orbits," Journal of the Aeronautical Sciences, Vol. 42, 1994, pp. 207-228.
33. SIMÓ C. "Effective Computations in Hamiltonian Dynamics," Cent ans après les Méthodes Nouvelles de H. Poincaré, Société Mathématique de France, 1996, pp. 1-23.
34. BROER, H., and SIMO, C. "Resonance Tongues in Hill's Equations: A Geometric Approach," Preprint, 1997.
35. BROER, H. SIMÓ, C., and TATJER, J. C. "Towards Global Models Near Homoclinic Tangencies of Dissipative Diffeomorphisms," Nonlinearity, Vol. 11, 1998. pp. 667-770.
36. STOER, J. and BULIRSCH, R. Introduction to Numerical Analysis, Springer-Verlag, 1983.
37. SIMÓ, C. "Analytical and Numerical Computation of Invariant Manifolds," Modern Methods in Celestial Mechanics, D. Benest and C. Froeschlé (editors), Editions Frontières, 1990, pp. 285-330.
38. ANDREU, M. A. "The Quasibicircular Problem," Ph.D. dissertation, Dept. Matemàtica Aplicada I Anàlisi, Universitat de Barcelona, 1999.
39. ANDREU, M. A., and SIMÓ, C. "Translunar Halo Orbits in the Quasibicircular Model," To appear in The Dynamics of Small Bodies in the Solar System, Proceedings of NATO ASI, Maratea, Italy, A. Roy (editor), 1999, Kluwer (in press).