Heteroclinic connections between periodic orbits and resonance.pdf

CHAOS VOLUME 10, NUMBER 2 JUNE 2000 Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics Wang Sang Koona) Control and Dynamical Systems, Caltech 107-81, Pasadena, California 91125 Martin W. Lob) Navigation and Mission Design, Jet Propulsion Laboratory M/S: 301-142, 4800 Oak Grove Drive, Pasadena, California 91109-8099 Jerrold E. Marsdenc) Control and Dynamical Systems, Caltech 107-81, Pasadena, California 91125 Shane D. Rossd) Control and Dynamical Systems, Caltech 107-81, Pasadena, California 91125 Received 21 May 1999; accepted for publication 6 December 1999 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 L 1 and the other around L 2 , 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 L 1 and L 2 as well as the aforementioned heteroclinic connection are fundamental tools that can