This is a preview of subscription content, log in via an institution to check access.
References
Arnold, V., Arnold, I., (1963a): “On a theorem of Liouville concerning integrable problems of dynamics”,Sib. mathem. zh.,4, 2.
Arnold, V., Arnold, I., (1963b): “Proof of A. N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in the Hamiltonian.”,Russian Math. Surv.,18, No. 5, 9–36.
Arnold, V., Arnold, I., (1964): “Instability of dynamical systems with several degrees of freedom”,Sov. Math. Dokl.,5, N1, 581–585.
Delaunay, C., (1867): “Theorie du mouvement de la Lune”,Mem. Acad. Sci., Paris,29.
Ferraz-Mello, S., (1989): “A semi-numerical expansion of the averaged disturbing function for some very-high-eccentricity orbits.”,Celest. Mech.,45, 65–68.
Giorgilli, A., (1989): “New insights on the stability problem from recent results in classical perturbation theory”, inModern methods in Celestial Mechanics, D. Benest and Cl. Froeschlé eds., Editions Frontières.
Henrard, J., (1990): “A semi-numerical perturbation method for separable Hamiltonian systems.”,Celest. Mech.,49, 43–67.
Kolmogorov, A., Kolmogorov, N., (1954): “Preservation of conditionally periodic movements with small change in the Hamiltonian function”,Dokl. Akad. Nauk SSSR,98, 527–530; English translation inLecture notes in Physics, N.93, 51–56, Casati, G. and Ford, J. eds.
Lichtenberg, A.J., and Lieberman, M.A., (1983): “Regular and stochastic motion.”,Springer Verlag ed.
Moons, M., and Henrard, J., (1992): “Surfaces of sections in the Miranda-Umbriel 1/3 inclination problem”, in preparation.
Morbidelli, A., (1992): “On the successive eliminations of perturbation harmonics.”,Celest. Mech., in press.
Morbidelli, A., and Giorgilli, A., (1992): “A quantitative perturbation theory by successive elimination of harmonics.”,Celest. Mech., in press.
Moser, J., (1962): “On invariant curves of area-preserving mappings of an annulus”,Nachr. Akad. Wiss. Gottingen, Math. Phys. 2, 1.
Nekhoroshev, N., Nekhoroshev, N., (1971): “Behaviour of Hamiltonian systems clos to integrable”,Funct. An. and Appl.,5, 338–339.
Nekhoroshev, N., Nekhoroshev, N., (1977): “Exponential estimate of the stability time of near-integrable Hamiltonian systems”,Russ. Math. Survey,32, N.6, 1–65.
Nekhoroshev, N., Nekhoroshev, N., (1979): “Exponential estimate of the stability time of near-integrable Hamiltonian systems, II”,Trudy. Sem. Petrovs.,5, 5–50 (in Russian).
Poincaré, H., (1892):Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars, Paris.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morbidelli, A. An introduction to Hamiltonian dynamical systems and practical perturbation methods: New insight by successive elimination of perturbation harmonics. Celestial Mech Dyn Astr 56, 177–190 (1993). https://doi.org/10.1007/BF00699730
Issue Date:
DOI: https://doi.org/10.1007/BF00699730