Abstract
We study Harrington's Hamiltonian in the Hill approximation of the stellar problem of three bodies in order to clarify and sharpen a qualitative analysis made by Lidov and Ziglin. We show how the orbital space after four reductions is a two-dimensional sphere, Harrington's Hamiltonian defining a biparametric dynamical system. We produce the diagrams corresponding to each type of phase flow according to a complete discussion of all possible local and global bifurcations determined by the four integrals of the system.
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Ferrer, S., Osácar, C. Harrington's Hamiltonian in the stellar problem of three bodies: Reductions, relative equilibria and bifurcations. Celestial Mech Dyn Astr 58, 245–275 (1994). https://doi.org/10.1007/BF00691977
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DOI: https://doi.org/10.1007/BF00691977