THE DYNAMICS OF RESONANT CAPTURE

Resonant capture describes the behavior of a weakly coupled multi-degr ee-of-freedom system when two or more of its uncoupled frequencies bec ome locked in resonance. Flow on the region of phase space near the re sonance (the resonance manifold) involves a region bounded by a separa trix in the uncoupled (epsilon = 0) system. Capture corresponds to mot ions which appear to cross into the interior of the separated region f or epsilon > 0. We offer two approximate methods for estimating which initial conditions lead to capture: an energy method and a perturbatio n method based on invariant manifold theory. These methods are applied to a model problem involving the spinup of an unbalanced rotor attach ed to an elastic support.