Harrington's Hamiltonian in the stellar problem of three bodies: Reductions, relative equilibria and bifurcations

Details Harrington's Hamiltonian in the stellar problem of three bodies: Reductions, relative equilibria and bifurcations Harrington's Hamiltonian in the stellar problem of three bodies: Reductions, relative equilibria and bifurcations

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..245f&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, vol. 58, no. 3, p. 245-275

Mathematics

7

Center Of Gravity, Hamiltonian Functions, Kepler Laws, Stellar Orbits, Three Body Problem, Triple Stars, Branching (Mathematics), Canonical Forms, Transformations (Mathematics)

Scientific paper

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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