Splitting of separatrices in the rapidly forced Duffing oscillator

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The splitting of the stable and unstable manifolds of the rapidly forced Duffing oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.

Original languageEnglish (US)
Title of host publicationNonlinear Vibrations
EditorsMo Shahinpoor, H.S. Tzou
PublisherPubl by ASME
Pages249-255
Number of pages7
ISBN (Print)0791811719
StatePublished - Dec 1 1993
Event14th Biennial Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA
Duration: Sep 19 1993Sep 22 1993

Publication series

NameAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Volume54

Other

Other14th Biennial Conference on Mechanical Vibration and Noise
CityAlbuquerque, NM, USA
Period9/19/939/22/93

ASJC Scopus subject areas

  • Engineering(all)

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