Abstract
A second-order libration solution of theIdeal Resonance Problem is construeted using a Lie-series perturbation technique. The Ideal Resonance Problem is characterized by the equations
together with the property thatB x vanishes for some value ofx. Explicit expressions forx andy are given in terms of the mean elements; and it is shown how the initial-value problem is solved. The solution is primarily intended for the libration region, but it is shown how, by means of a substitution device, the solution can be extended to the deep circulation regime. The method does not, however, admit a solution very close to the separatrix. Formulae for the mean value ofx and the period of libration are furnished.
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Jupp, A.H. A second-order solution of the Ideal Resonance Problem by Lie series. Celestial Mechanics 5, 8–26 (1972). https://doi.org/10.1007/BF01227819
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DOI: https://doi.org/10.1007/BF01227819