Periodic Solutions of a System of Coupled Oscillators Near Resonance

Details Periodic Solutions of a System of Coupled Oscillators Near Resonance Periodic Solutions of a System of Coupled Oscillators Near Resonance

1993-05-17

arxiv.org/abs/chao-dyn/9305007v1

Nonlinear Sciences

Chaotic Dynamics

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Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally nondegenerate. The bifurcation function whose zeros are the bifurcation points for families of perturbed periodic solutions is determined. This result is applied to find the periodic solutions near resonance for a two degree of freedom mechanical system modeling a rotor interacting with an elastic support.

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