Three-Dimensional Nonlinear Stability Analysis of the Sun-Perturbed Earth-Moon Equilateral Points.

by Hans B. Schechter

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A nonlinear study of the long period features of the motion of a particle in the earth-moon system, near the equilateral libration point. Such effects stem from excitations close to the particle's natural frequencies, introduced by the presence of resonance terms in the internal and external force fields. Nonlinearities up to the fourth order in displacements from the equilateral, and solar terms of comparable magnitude, were retained. The importance of nonlinear coupling of out-of-plane motion with in-plane motion was investigated, and the existence of some equilibrium solutions was established, and insight regarding the geometry of motion along the corresponding periodic elliptic particle orbits was obtained, providing qualitative and quantitative information concerning their stability. 22 pp. Ref.

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