The Modal Solution to the Moon's Orbit Using Canonical Floquet Perturbation Theory
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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Using the restricted three body problem, the equations of motion EOM and Hamiltonian are computed for the moons orbit in physical variables. A periodic orbit is found in the vicinity of the moons 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 moons orbit. Once satisfied that the moons 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 moons orbit given enough expansion terms.
- Celestial Mechanics