On the vertical families of two-dimensional tori near the triangular points of the bicircular problem

Celestial Mechanics and Dynamical Astronomy

Volumn 76, Issue 1, 2000, Pages 35-54

  Castellà, Enric ^a,b   Jorba, Àngel ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Bicircular problem; Cantor families of lower dimensional tori; Equilateral points; Lagrangian points; Quasi periodic orbits; Trojan motion

Indexed keywords

EID: 0040845842     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008321605028     Document Type: Article

References (22)

1. 5 in the spatial restricted three-body problem', Regular Chaotic Dynam. 3 (1998), 56-72.
2. Celletti, A. and Giorgilli, A.: 'On the stability of the Lagrangian points in the spatial restricted three body problem', Celest. Mech. & Dyn. Astr. 50 (1991), 31-58.
3. Díez, C., Jorba, À. and Simó, C.: 'A dynamical equivalent to the equilateral libration points of the Earth-Moon system', Celest. Mech. & Dyn. Astr. 50 (1991), 13-29.
4. Giorgilli, A., Delshams, A., Fontich, E., Galgani, L. and Simò, 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(1) (1989), 167-198.
5. 4 in the Earth-Moon system', Proceedings of the 3rd International Symposium on Spacecraft Flight Dynamics, ESA Publications Division, ESTEC, Noordwijk, Holland, 1991, pp. 35-41.
6. Gómez, G., Jorba, À., Masdemont, J. and Simó, C.: Study of Poincaré Maps for Orbits near Lagrangian Points, ESOC Contract 9711/91/D/IM(SC), Final Report, 1993.
7. Gómez, G., Llibre, J., Martínez, R. and Simó, C.: 'Study on orbits near the triangular libration points in the perturbed restricted three-body problem', ESOC Contract 6139/84/D/JS(SC), Final Report, 1987.
8. Henrard, J.: 'Lyapunov's center theorem for resonant equilibrium', J. Diff. Eq. 14 (1973), 431-441.
9. Jorba, À.: 'A preliminary numerical study on the existence of stable motions near the triangular points of the real Earth-Moon system', preprint, 1999.
10. Jorba, À.: 'Numerical computation of the normal behaviour of invariant curves of higher dimensional maps', in progress.
11. Jorba, À. and Villanueva, J.: 'On the persistence of lower dimensional invariant tori under quasi-periodic perturbations', J. Nonlinear Sci. 7 (1997), 427-473.
12. Jorba, À. and Villanueva, J.: 'On the normal behaviour of partially elliptic lower dimensional tori of hamiltonian systems', Nonlinearity 10 (1997), 783-822.
13. Jorba, À. and Villanueva, J.: 'Numerical computation of normal forms around some periodic orbits of the restricted three body problem', Physica D 114 (1998), 197-229.
14. Meyer, K. R. and Hall, G. R.: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer-Verlag, 1992.
15. Sevryuk, M. B.: 'Excitation of elliptic normal modes of invariant tori in Hamiltonian systems', In A. Khovanskij et al. (eds), Topics in Singularity Theory. V.I. Arnold's 60th Anniversary Collection, Amer. Math. Soc. Transl., Ser. 2, Am. Math. Soc. 180(34) (1997), 209-218.
16. Sevryuk, M. B.: 'Invariant tori of intermediate dimensions in Hamiltonian systems', Regul. Khaoticheskaya Din. 3 (1998), 39-48.
17. Siegel, C. L. and Moser, J.: Lectures on Celestial Mechanics, Springer-Verlag, 1971.
18. Simó, C.: 'Estabilitat de sistemes hamiltonians', Mem. de la Real Acad. de Ciencias y Artes de Barcelona, Vol. XLVIII, no. 7, 1989.
19. Simó, C.: 'Effective computations in celestial mechanics and astrodynamics', In V. V. Rumyantsev and A. V. Karapetyan (eds), Modern Methods of Analytical Mechanics and their Applications, CISM Courses and Lectures Vol. 387, Springer, 1998.
20. Simó, C., Gòmez, G., Jorba, À. and Masdemont, J.: 'The bicircular model near the triangular libration points of the RTBP', In A. E. Roy and B. A. Steves (eds), From Newton to Chaos, Plenum Press, New York, 1995, pp. 343-370.
21. Szebehely, V.: Theory of Orbits, Academic Press, 1967.
22. http://ssd.jpl.nasa.gov/horizons.html