Abstract
Resonant capture describes the behavior of a weakly coupled multi-degree-of-freedom system when two or more of its uncoupled frequencies become locked in resonance. Flow on the region of phase space near the resonance (the resonance manifold) involves a region bounded by a separatrix in the uncoupled (ε = 0) system. Capture corresponds to motions which appear to cross into the interior of the separated region for ε > 0.
We offer two approximate methods for estimating which initial conditions lead to capture: an energy method and a perturbation method based on invariant manifold theory. These methods are applied to a model problem involving the spinup of an unbalanced rotor attached to an elastic support.
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© 1995 Springer Science+Business Media Dordrecht
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Quinn, D., Rand, R., Bridge, J. (1995). The Dynamics of Resonant Capture. In: Bajaj, A.K., Shaw, S.W. (eds) Advances in Nonlinear Dynamics: Methods and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0367-1_1
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DOI: https://doi.org/10.1007/978-94-011-0367-1_1
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