Generating planar periodic orbits of the Hill’s problem
We consider the planar Hill’s problem which is a limiting case of the circular restricted three–body problem. The system of equations of motion of the problem can be considered either as a singularly perturbed linear Hamiltonian system (called the intermediate H´enon problem) or as a regularly perturbed Kepler problem in the uniformly rotating (sinodical) frame. Generating planar periodic orbits of the Hill’s problem are investigated with the method of normal form. It was shown that in the case of unperturbed problem being intermediate Henon problem, the only generating solution is the double symmetric elliptical reverse orbit which generates the known family ƒ. In the case of the generating problem being the sinodical Kepler problem there are a
countable set of generating families, which include both symmerical and asymetrical
periodic orbits. Asymptotic forms for period and stability index of generating solutions were obtained.
Mathematical problems and theory of numerical methods