Nonholonomic reduction
type: Item
instance of: scholarly article
title: Nonholonomic reduction
zbMATH Open document ID: 0798.58026
DOI: 10.1016/0034-4877(93)90073-N
published in: Reports on Mathematical Physics
publication date: 1994-06-16T00:00:00Z
review text: This paper addresses the problem of nonholonomic reduction of Hamiltonian systems in the presence of symmetry. The authors describe the structure of Hamiltonian systems with constraints in a manner that facilitates understanding of the reduction process. For simplicity of exposition, the authors examine only Hamiltonian systems that come from a Lagrangian system (of the form kinetic energy minus potential energy) where the Legendre transformation is a diffeomorphism and the constraints are independent of time. The reduction of nonholonomic systems by symmetry is formulated in such a way that it parallels the standard theory of reduction of symplectic manifolds with symmetry. In so doing, the authors show that the constraints in the Hamiltonian theory play a dual role in which they define both a constraint manifold and a horizontal distribution on which a distributional form of Hamilton's equations hold. The authors illuminate their results using the example of a free particle subjected to a nonholonomic constraint.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 563469
zbMATH Keywords: nonholonomic constraints
zbMATH Keywords: reduction by symmetry
zbMATH Keywords: Hamiltonian systems
author: Larry Bates
author: J. Śniatycki
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
cites work: Q4166258
cites work: Closed forms on symplectic fibre bundles
cites work: Reduction of some classical non-holonomic systems with symmetry
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q5657709
cites work: Q5329596
cites work: Analytical dynamics of discrete systems
cites work: Conditions on a connection to be a metric connection
cites work: Non-holonomic Chaplygin systems
cites work: Hamiltonian systems with constraints and their meaning in mechanics
full work available at URL: 0034-4877(93)90073-n
OpenAlex ID: W4243502888
description: scientific article; zbMATH DE number 563469