Asymptotic motions of nonholonomic Chaplygin systems
type: Item
instance of: scholarly article
title: Asymptotic motions of nonholonomic Chaplygin systems
zbMATH Open document ID: 0724.70012
DOI: 10.1007/BF01060385
author: D. Kharzeev
published in: Ukrainian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The existence of asymptotic motions in the neighborhood of an equilibrium configuration that is a center of attraction for them, is of great interest because for a good class of holonomic conservative systems these motions are accompanied by instability of the equilibrium configuration as well as its roughness, i.e., its indestructibility with a sufficiently small ``stirring'' of the corresponding equations. It turns out that an analogous situation holds for nonholonomic Chaplygin systems as well. In this paper we are able to prove, for a certain class of such systems, developing the approach proposed by the author in Ukr. Mat. Zh. 37, No.1, 124-127 (1985), the existence of phase trajectories bordering on an equilibrium configuration as \(t\to \infty\) and \(t\to -\infty\), and the rough instability of the latter.
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 4195246
zbMATH Keywords: existence of asymptotic motions
zbMATH Keywords: equilibrium configuration
zbMATH Keywords: center of attraction
zbMATH Keywords: nonholonomic Chaplygin systems
MaRDI profile type: Publication
cites work: Q3264374
cites work: Q5657709
full work available at URL: https://doi.org/10.1007/bf01060385
OpenAlex ID: W2013072704
description: scientific article; zbMATH DE number 4195246