Heteroclinic connections between
periodic orbits and resonance transitions in celestial mechanics
Koon, WS;
Lo, MW;
Marsden, JE;
Ross, SD;
CHAOS
10(2), 427-469, JUN 2000
Abstract:
In this paper we apply dynamical systems techniques to the problem of
heteroclinic connections and resonance transitions in the planar circular restricted three-body
problem. These related phenomena have been of concern for some time in topics such as the capture
of comets and asteroids and with the design of trajectories for space missions such as the
Genesis Discovery Mission. The main new technical result in this paper is the numerical
demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one
around the libration point L1 and the other around L2, with the two periodic orbits having the
same energy. This result is applied to the resonance transition problem and to the explicit
numerical construction of interesting orbits with prescribed itineraries. The point of view
developed in this paper is that the invariant manifold structures associated to L1 and L2 as
well as the aforementioned heteroclinic connection are fundamental tools that can aid in
understanding dynamical channels throughout the solar system as well as transport between the
"interior" and "exterior" Hill's regions and other resonant phenomena.
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