Abstract
In the presence of a single small-integer near commensurability of orbital period, the construction of a complete formal solution of the equations for the mutual perturbations in a planetary or satellite system, entirely in periodic terms, can be carried out after the use of a transformation of the variables which brings the quadratic terms of the Hamiltonian to a suitable normal form. A method for finding such a transformation is described.
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References
Message, P.J., 1982a: “Asymptotic Series for Planetary Motion in Periodic Terms in Three Dimensions”, in Celestial Mechanics, 26, 25–39.
Message, P.J., 1982b: “Some Aspects of Motion in the General Planar Problem of Three Bodies; in Particular in the Vicinity of Periodic Solutions Associated with near Small-Integer Commensurabilities of Orbital Period”, in “Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics” (Proceedings of the N.A.T.O. Advanced Study Institute, 1981) ed. V. Szebehely (Reidel), 77–101.
Message, P.J., 1988: “Planetary Perturbation Theory from Lie Series, including Resonance and Critical Arguments”, in “Long-Term Dynamical Behaviour of Natural and Artificial n-Body Systems” (Proceedings of the N.A.T.O. Advanced Study Institute, 1987) ed. A.E. Roy (Reidel).
Poincaré. H, 1893: “Les Méthodes Nouvelles de la Mécanique Célèste” (Gauthier-Villars).
Siegel, C.L. and Moser, J.K., 1971: “Lectures on Celestial Mechanics”, (Springer-Verlag).
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© 1988 Kluwer Academic Publishers
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Message, P.J. (1988). Normal Co-Ordinates and Asymptotic Expansions in Resonance Cases in Celestial Mechanics. In: Dvorak, R., Henrard, J. (eds) Long Term Evolution of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2285-3_10
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DOI: https://doi.org/10.1007/978-94-009-2285-3_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7525-1
Online ISBN: 978-94-009-2285-3
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