Mathematics
Scientific paper
Oct 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28...83l&link_type=abstract
(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani
Mathematics
9
Existence Theorems, Three Body Problem, Collisions, Manifolds (Mathematics), Mass, Orbits, Two Body Problem
Scientific paper
Some aspects of the restricted three-body problem when the mass parameter is sufficiently small are discussed. The global flow of the two-body rotating problem is described and used for the analysis of the collision and parabolic orbits when the mass parameter is small enough. Four theorems dealing with the orbits of the three bodies are presented and proved. The two-body problem is analyzed for the cases when the Jacobian constant is between zero and three, equal to three, and greater than three. It is shown for the two-body rotating problem and for the restricted three-body problem that the sets of orbits which end or begin at collision with one of the primaries are respectively the stable and unstable invariant manifold associated to a convenient invariant set. It is proved that these orbits are topologically a cylinder. Finally, the restricted three-body problem in a rotating coordinate system of frequency equal to one is considered, and a theorem is produced.
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