Three-dimensional periodic solutions around equilibrium points in Hill's problem

Details Three-dimensional periodic solutions around equilibrium points in Hill's problem Three-dimensional periodic solutions around equilibrium points in Hill's problem

Mar 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35..257z&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 35, March 1985, p. 257-267.

Physics

7

Celestial Mechanics, Hill Method, Lagrangian Equilibrium Points, Three Body Problem, Cartesian Coordinates, Equations Of Motion, Orbit Calculation, Periodic Variations, Perturbation Theory, Secular Variations

Scientific paper

The three-dimensional periodic solutions originating at the equilibrium points of Hill's limiting case of the restricted three-body problem, are studied. Fourth-order parametric expansions by the Lindstedt-Poincaré method are constructed for them. The two equilibrium points of the problem give rise to two exactly symmetrical families of three-dimensional periodic solutions. The family HL2νe originating at L2 is continued numerically and is found to extend to infinity. The family originating at L1 behaves in exactly the same way. All orbits of the two families are unstable.

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