A Second-Order Solution of the Ideal Resonance Problem by Lie Series

Details A Second-Order Solution of the Ideal Resonance Problem by Lie Series A Second-Order Solution of the Ideal Resonance Problem by Lie Series

Jan 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...5....8j&link_type=abstract

Celestial Mechanics, Volume 5, Issue 1, pp.8-26

Physics

22

Scientific paper

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 begin{gathered} - F = B(x) + 2μ ^2 A(x)sin^2 y, \ dot x = - Fy,dot y = Fx, \ 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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