Melnikov's method for a general nonlinear vibro-impact oscillator
type: Item
instance of: scholarly article
title: Melnikov's method for a general nonlinear vibro-impact oscillator
zbMATH Open document ID: 1176.34052
author: Wei Xu
author: Jinqian Feng
author: H. W. Rong
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-06-09T00:00:00Z
review text: The classical Melnikov's method is applied to a second order differential equation with impact effects. The equation is a perturbation of a Hamiltonian system with a homoclinic orbit to the origin. Then the first-order Melnikov function can be obtained analytically in the usual way. The method is applied to a double-well Duffing oscillator with impacts, thus obtaining a chaotic threshold, and complemented with some numerical computations.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34A26
zbMATH DE Number: 5563045
zbMATH Keywords: vibro-impact oscillator
zbMATH Keywords: non-smooth system
zbMATH Keywords: Melnikov's method
zbMATH Keywords: homoclinic orbit
MaRDI profile type: Publication
full work available at URL: j.na.2008.10.120
OpenAlex ID: W2058647515
cites work: A Periodically Forced Impact Oscillator With Large Dissipation
cites work: Nonsmooth mechanics. Models, dynamics and control.
cites work: Stick-slip vibrations and chaos
cites work: On the origin and bifurcations of stick-slip oscillations
cites work: Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact micro\-actuators
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Bifurcations of subharmonics
cites work: The transition to chaos in a simple mechanical system
cites work: Non-smooth dynamical systems
cites work: Melnikov method for discontinuous planar systems
cites work: Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
cites work: MELNIKOV'S METHOD AND STICK–SLIP CHAOTIC OSCILLATIONS IN VERY WEAKLY FORCED MECHANICAL SYSTEMS
cites work: Chaos prediction in the Duffing-type system with friction using Melnikov's function
cites work: How to predict stick-slip chaos in \(R^4\)
cites work: Analytical prediction of stick-slip chaos in a double self-excited Duffing-type oscillator
cites work: Q4531878
DOI: 10.1016/J.NA.2008.10.120
description: scientific article; zbMATH DE number 5563045