On the realization of holonomic constraints
type: Item
instance of: scholarly article
title: On the realization of holonomic constraints
zbMATH Open document ID: 0759.70011
DOI: 10.1016/0021-8928(90)90121-P
published in: Journal of Applied Mathematics and Mechanics
publication date: 1992-09-26T00:00:00Z
review text: The general theorem on the realization of holonomic constraints with the help of elastic forces directed towards the configurational manifold of the constrained system refers to Courant. There exist generalizations of the main result, all assuming that the system in question is conservative. The main result of this paper is that the Courant's theorem is valid without this assumption. More precisely, a free system \((\partial E/\partial \dot r)^ .-\partial E/\partial r=F-N\partial w/\partial r\) with sufficiently large \(N\) and \(W\) having its minimum on the manifold of constraints, is considered. Let \(r_ N(t)\) and \(r_ \infty(t)\) be the evolutions of the free system and the constrained system, respectively. Under certain nonrestrictive assumptions it is proved that for \(0\leq t\leq 1\) \(r_ N(t)=r_ \infty(t)+O(N^{-1})\), \(\dot r_ N(t)=\dot r_ \infty(t)+O(N^{-1/2})\).
Mathematics Subject Classification ID: 70F20
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 56386
zbMATH Keywords: asymptotics under strong elastic forces
zbMATH Keywords: Courant's theorem
author: Valery V. Kozlov
author: Anatoly Neishtadt
MaRDI profile type: Publication
cites work: Motion under a strong constraining force
cites work: Q3908204
cites work: Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. I
full work available at URL: 0021-8928(90)90121-p
OpenAlex ID: W1964272635
description: scientific article; zbMATH DE number 56386