Problems and progress in nonholonomic reduction
type: Item
instance of: scholarly article
title: Problems and progress in nonholonomic reduction
zbMATH Open document ID: 1014.37041
DOI: 10.1016/S0034-4877(02)80014-3
published in: Reports on Mathematical Physics
publication date: 2003-01-22T00:00:00Z
review text: The present paper is an excellent survey on analogies between Hamiltonian and nonholonomic systems, with a special view to reduction schemes in presence of symmetry. Several citations are from the historical founders of the subject, e.g. Appell (1899), Chaplygin (around the same time), Jacobi (1837, 1842), Liouville (1855), Arnold (1865), Meyer (1973), Marsden and Weinstein (1974), and also from the recent papers of the author et al. [for example Rep. Math. Phys. 42, No. 1-2, 231--247 (1998; Zbl 0931.37022) and Rep. Math. Phys. 37, No. 1-3, 295--308 (1996; Zbl 0887.58016)]. The paper begins with two examples, one physical (the rattleback) and one mathematical, and ends with a list of five open problems which offers good starting points for a future research.
Mathematics Subject Classification ID: 37J60
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 70F25
zbMATH DE Number: 1857351
zbMATH Keywords: nonholonomic mechanics
zbMATH Keywords: complete integrability
zbMATH Keywords: symmetry and reduction
zbMATH Keywords: survey
author: Larry Bates
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
cites work: Q4174811
cites work: Q5554207
cites work: Examples of singular nonholonomic reduction
cites work: Examples of gauge conservation laws in nonholonomic systems
cites work: Proper group actions and symplectic stratified spaces
cites work: On action-angle variables
cites work: Nonholonomic reduction
cites work: The rigid body dynamics of unidirectional spin
cites work: On global action-angle coordinates
cites work: Orbifolds as configuration spaces of systems with gauge symmetries
cites work: Q4239965
cites work: Reduction of some classical non-holonomic systems with symmetry
cites work: Hamiltonian torus actions on symplectic orbifolds and toric varieties
cites work: Q3785520
cites work: Generic Hamiltonian dynamical systems are neither integrable nor ergodic
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q4045361
cites work: Pseudointegrable systems in classical and quantum mechanics
cites work: Stratified symplectic spaces and reduction
Wikidata QID: Q125817511
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description: scientific article; zbMATH DE number 1857351