Limit cycles in the equation of whirling pendulum with autonomous perturbation.
type: Item
instance of: scholarly article
title: Limit cycles in the equation of whirling pendulum with autonomous perturbation.
zbMATH Open document ID: 1060.34504
DOI: 10.1023/A:1023080513150
author: Hana Lichardová
published in: Applications of Mathematics
publication date: 2005-05-04T00:00:00Z
full work available at URL: https://eudml.org/doc/33034
review text: The paper deals with a two-parameter Hamiltonian system with an autonomous perturbation which models a whirling pendulum. Using the Melnikov function method, the author proves the existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters. After a short description of local bifurcations of the system, the global analysis of the phase portrait is given by means of the study of properties of the Melnikov function whose zeros correspond to limit cycles. The needed properties of the Melnikov function the author gets either by a direct study of corresponding elliptic integrals and by the Li and Zhang criterion, which allows one to examine the monotonicity of the ratio of two Abelian integrals without calculating them.
reviewed by: Irena Rachůnková
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 70K05
zbMATH DE Number: 2165523
zbMATH Keywords: whirling pendulum
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: autonomous perturbation
zbMATH Keywords: Melnikov function
zbMATH Keywords: limit cycle
zbMATH Keywords: homoclinic orbit
zbMATH Keywords: elliptic integral
MaRDI profile type: Publication
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OpenAlex ID: W181417229
description: scientific article; zbMATH DE number 2165523