Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces.

The problem of directing a trajectory of a chaotic dynamical system to a target has been previously considered, and it has been shown that chaos allows targeting using only small controls. In this paper we consider targeting in a Hamiltonian system, whose phase space contains a mixture of regular quasi-periodic and chaotic regions. A multistep forward-backward method targeting strategic intermediate points is found to be efficient and robust. It takes full advantage of the phase space structure and is believed to yield optimal transport times. It is robust under the influence of small noise and small modeling errors and recovers from temporary loss of control. Two illustrative examples, the standard map and the restricted circular three body problem, are presented. (The latter corresponds to motion of a space probe in the presence of the earth and the moon.) Comparisons are made of our method to other targeting strategies. (c) 1997 American Institute of Physics.