The triple-collision manifold in the planar three-body problem

Details The triple-collision manifold in the planar three-body problem The triple-collision manifold in the planar three-body problem

Sep 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979crasm.289..365i&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie A - Sciences Mathematiques, vol. 289, no. 5, Sept. 24, 1979, p. 365-367. In

Mathematics

Celestial Mechanics, Collisions, Orbital Mechanics, Three Body Problem, Differential Equations, Manifolds (Mathematics)

Scientific paper

The triple-collision manifold in the planar three-body problem, which determines the behavior of triple-collision orbits, is defined on the basis of a previously derived system of sixth-order differential equations for the planar three-body problem. Double collisions are regularized in the system of eight differential equations, and an invariant phase-space manifold is defined in terms of the first integrals of energy and angular momentum of the system. The manifold is shown to be asymptotic for all triple collision orbits for which the square root of the moment of inertia approaches zero. The relation of the equilibrium points determined by the set of differential equations to the manifold is discussed, and the behavior of neighboring orbits is examined.

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