 9611 Luca Sbano, SISSA/ISAS Trieste Italia; email
 Noncollision periodic orbits with zero total angular momentum for
the Newtonian ThreeBody Problem
(65K, LAtex)
Jan 17, 96

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Abstract. We study the existence
of a periodic orbit without collisions,
with zero total angular momentum,
in the planar ThreeBody Problem
by means of Lagrangian reduction, variational methods and local analysis of the
flow.\par
In a preceeding paper \cite{luca} we described a class of compact set of
trajectories where to find minima for the Actionfunctional of the ThreeBody
Problem. In this paper we find critical points perturbatively in the masses, these critical points are in slightly
bigger compact sets.
We study a system composed of three bodies: two of them
with small {\it different} masses compared with the mass of the third
body. For the unperturbed problem we construct explicit solutions, which are
regular critical points for the unperturbed Actionfunctional.
These critical points can be {\it
continued} for sufficiently small values of the masses. We prove
the existence of periodic orbits without collisions.
Moreover for the full ThreeBody Problem on the manifold $J=0$ we verify
the existence of critical points at "infinity" composed of a Keplerproblem
and an "escaping" body.
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