Abstract
The third-order parametric expansions given by Buck in 1920 for the three-dimensional periodic solutions about the triangular equilibrium points of the restricted Problem are improved by fourthorder terms. The corresponding family of periodic orbits, which are symmetrical w.r.t. the (x, y) plane, is computed numerically for μ=0.00095. It is found that the family emanating from L4 terminates at the other triangular point L5 while it bifurcates with the family of three-dimensional periodic orbits originating at the collinear equilibrium point L3. This family consists of stable and unstable members. A second family of nonsymmetric three-dimensional periodic orbits is found to bifurcate from the previous one. It is also determined numerically until a collision orbit is encountered with the computations.
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