The modal solution to the Moon's orbit using canonical Floquet perturbation theory

Details The modal solution to the Moon's orbit using canonical Floquet perturbation theory The modal solution to the Moon's orbit using canonical Floquet perturbation theory

Dec 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993aifo.repts....v&link_type=abstract

M.S. Thesis Air Force Inst. of Tech., Wright-Patterson AFB, OH. School of Engineering.

Mathematics

Equations Of Motion, Floquet Theorem, Lunar Orbits, Moon, Perturbation Theory, Transformations (Mathematics), Differential Equations, Hamiltonian Functions, Perturbation, Three Body Problem

Scientific paper

Using the restricted three body problem, the equations of motion (EOM) and Hamiltonian are computed for the moon's orbit in physical variables. A periodic orbit is found in the vicinity of the moon's orbit, and classical Floquet theory is applied to the periodic orbit to give stability information and the complete solution to the equations of variation. Floquet theory also supplies a transformation from physical variables to modal variables. This transformation to modal variables is made canonical by constraining the initial transformation matrix to be symplectic. Actual lunar data is used to calculate the modes for the real moon's orbit. Once satisfied that the moon's real-world modes are in (or near) the linear regime of the periodic orbit, the modal EOM are found by doing a perturbation expansion on the new modal Hamiltonian. The modal results from the real lunar orbit are compared with the modal EOM/expansion results. The modal expansion proves to be an accurate solution to the moon's orbit given enough expansion terms.

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