On the dynamics of nonholonomic systems
type: Item
instance of: scholarly article
title: On the dynamics of nonholonomic systems
zbMATH Open document ID: 1184.70014
DOI: 10.1016/S0034-4877(08)00005-0
author: Natalia Sadovskaia
author: R. Ramirez
published in: Reports on Mathematical Physics
publication date: 2008-05-23T00:00:00Z
review text: The authors begin with a discussion of whether or not the equations of motion in nonholonomic mechanics can be derived from a variational principle in the usual sense. This question correlates with the role of transpositional relations. Namely, in nonholonomic mechanics the special form of the principle of stationary action depends on the transpositional relations. The aim of this paper is the treatment of transpositional relations in their most general form (a new form of equations of motion for nonholonomic systems with linear or nonlinear constraints, and also for holonomic systems, will follow immediately). By using Hamilton's principle with nonzero transpositional relations, the authors deduce the so-called \(A\)-model. In the \(A\)-model, the dependent variations always lead to nonzero transpositional relations, whereas transpositional relations corresponding to independent variations can be nonzero. It is shown how the well-known equations of motion for holonomic and nonholonomic mechanics can be derived from the A-model. The results are illustrated on various nonholonomic Chaplygin systems: the generalized Voronets-Chaplygin system, the generalized Chaplygin system, the Routh-Chaplygin system, and the Gaponov-Chaplygin system.
reviewed by: Jesús Marín-Solano
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70H25
Mathematics Subject Classification ID: 70H30
Mathematics Subject Classification ID: 70F20
zbMATH DE Number: 5278422
zbMATH Keywords: Chaplygin system
zbMATH Keywords: transpositional relations
zbMATH Keywords: Hamilton's principle
zbMATH Keywords: principle of stationary action
MaRDI profile type: Publication
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full work available at URL: s0034-4877(08)00005-0
OpenAlex ID: W2082918513
description: scientific article; zbMATH DE number 5278422