Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies

Details Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..37...27z&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 37, Sept. 1985, p. 27-46.

Mathematics

11

Lagrangian Equilibrium Points, Orbital Mechanics, Three Body Problem, Branching (Mathematics), Periodic Functions

Scientific paper

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 fourth-order terms. The corresponding family of periodic orbits, which are symmetrical with respect to the (x, y) plane, is computed numerically for mu = 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.

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