Symmetric and regularized coordinates on the plane triple collision manifold

Details Symmetric and regularized coordinates on the plane triple collision manifold Symmetric and regularized coordinates on the plane triple collision manifold

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28...69w&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani

Mathematics

5

Manifolds (Mathematics), Three Body Problem, Collisions, Coordinates, Equations Of Motion, Lagrangian Equilibrium Points, Transformations (Mathematics)

Scientific paper

Murnaghan's (1936) symmetric variables are employed in a description of the three-body planar problem which allows the elimination of nodes. After introducing Lemaitre's (1964) regularized variables, as well as their canonically conjugated momenta, McGehee's (1974) scaling transformation is applied to yield a system of seven differential equations with two first integrals for the five-dimensional triple collision manifold T. The zero angular momentum solutions form a four-dimensional invariant submanifold N, contained in T, represented by six differential equations with polynomial right-hand sides. The manifold N is of the topological type S-squared x S-squared with 12 points removed, and contains all five restpoints. The flow of T is gradient-like, with a Lyapunov function which is stationary in the 40 restpoints.

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