Electronic Resource
Springer
Nonlinear dynamics
8 (1995), S. 1-20
ISSN:
1573-269X
Keywords:
Resonance
;
capture
;
separatrix
;
invariant
;
manifold
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00045004
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