The triple collision manifold

Details The triple collision manifold The triple collision manifold

Mar 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979crasm.288..635w&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie A - Sciences Mathematiques, vol. 288, no. 12, Mar. 26, 1979, p. 635-637. In

Mathematics

1

Astronomical Coordinates, Collision Parameters, Manifolds (Mathematics), Three Body Problem, Angular Momentum, Celestial Mechanics, Differential Equations, Hamiltonian Functions

Scientific paper

The submanifold with energy and angular momentum equal to zero in six dimensional space of the triple collision manifold in the planar three body problem is described by means of symmetric and regularized variables. The Hamiltonian of the three body problem is written in coordinates corresponding to the sides and angles of the triangle formed by the three bodies and in canonically conjugate variables. Binary collisions are regularized by the Lemaitre transformation, transforming the Hamiltonian into a system of six first order differential equations defining the triple collision manifold. The integrals of the differential equations are presented.

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