Planetary perturbation theory from Lie series, including resonance and critical arguments.

Details Planetary perturbation theory from Lie series, including resonance and critical arguments. Planetary perturbation theory from Lie series, including resonance and critical arguments.

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ltdb.conf...47m&link_type=abstract

NATO Advanced Study Institute on Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, p. 47 - 72

Computer Science

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Planetary Theories: Commensurabilities, Planetary Theories: Resonances, Planetary Theories: Perturbation Theory

Scientific paper

The Lie series transformation method is used to derive the main properties of the first- and second-order periodic terms in planetary perturbation theory, indicating how periodic terms of further orders may be derived. Then the formal solution of the complete problem, including long-term changes, is derived, by use of further transformations, including a further Lie series transformation to derive the complete expressions for the long-period variations. The solution thus obtained expresses the orbital elements in series entirely of periodic terms, some of the frequencies being those of the long-period "secular" variations. It is seen how near-resonance conditions present difficulties, and it is shown how, in the case of a single close resonance, they may be surmounted by an appropriate modification of the method.

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