Effect of initial configurations on libration point motion

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Abstract In the restricted three-body problem, motion about the triangular Lagrange libration points is stable, under certain conditions, in the sense that if a particle is “slightly” disturbed it will still remain “close” to the original libration point. In the case of the earth-moon system, the sun exerts a strong perturbing influence and the equilibrium points no longer exist. To investigate stability in this case, a very restricted four-body problem is formulated and “stable” trajectories are found. Their existence is shown to be markedly influenced by the initial configuration of the three large bodies. The stable initial state conditions are found from a first-order variational solution and later refined by numerical integration of the equations of motion. Real world trajectories are shown to exhibit qualitatively the same configuration effects.