Asymptotic analysis of strongly nonlinear oscillators
type: Item
instance of: scholarly article
title: Asymptotic analysis of strongly nonlinear oscillators
zbMATH Open document ID: 0585.34039
DOI: 10.1007/BF01895378
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1985-01-01T00:00:00Z
review text: In the paper the asymptotic method is applied for the analysis of a strongly nonlinear autonomous oscillator characterised by the differential equation \(\ddot u+g(u)=\epsilon f(u,\dot u)\) with a small parameter \(\epsilon >0\). The equations for the amplitude and phase factor are obtained and the amplitude and stability of the corresponding limit cycles are determined.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3937602
zbMATH Keywords: second order differential equation
zbMATH Keywords: strongly nonlinear autonomous oscillator
zbMATH Keywords: phase factor
zbMATH Keywords: limit cycles
author: Shiqiang Dai
reviewed by: Janusz Mika
MaRDI profile type: Publication
cites work: Perturbation methods in applied mathematics
cites work: A perturbation method for nonlinear dispersive wave problems
cites work: Q4151274
cites work: Non-linear oscillator limit cycle analysis using a time transformation approach
cites work: Q5615009
full work available at URL: https://doi.org/10.1007/bf01895378
OpenAlex ID: W2326224294
description: scientific article; zbMATH DE number 3937602