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Nonholonomic dynamical reduction of open-chain multi-body systems: A geometric approach
Institute for Aerospace Studies, University of Toronto.
Institute for Aerospace Studies, University of Toronto.ORCID iD: 0000-0003-4977-6339
2014 (English)In: Mechanism and machine theory, ISSN 0094-114X, E-ISSN 1873-3999, Vol. 82, p. 231-255Article in journal (Refereed) Published
Abstract [en]

This paper studies the geometry behind nonholonomic Hamilton's equation to present a two-stage reduction procedure for the dynamical equations of nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. In this process, we use the Chaplygin reduction and an almost symplectic reduction theorem. We first restate the Chaplygin reduction theorem on cotangent bundle for nonholonomic Hamiltonian mechanical systems with symmetry. Then, under some conditions we extend this theorem to include a second reduction stage using an extended version of the symplectic reduction theorem for almost symplectic manifolds. We briefly introduce the displacement subgroups and accordingly open-chain multi-body systems consisting of such joints. For a holonomic open-chain multi-body system, the relative configuration manifold corresponding to the first joint is a symmetry group. Hence, we focus on a class of nonholonomic distributions on the configuration manifold of an open-chain multi-body system that is invariant under the action of this group. As the first stage of reduction procedure, we perform the Chaplygin reduction for such systems. We then introduce a number of sufficient conditions for a reduced system to admit more symmetry due to the action of the relative configuration manifolds of other joints. Under these conditions, we present the second stage of the reduction process for nonholonomic open-chain multi-body systems with multi-degree-of-freedom joints. Finally, we explicitly derive the reduced dynamical equations in the local coordinates for an example of a two degree-of-freedom crane mounted on a four-wheel car to illustrate the results of this paper.

Place, publisher, year, edition, pages
2014. Vol. 82, p. 231-255
Keywords [en]
Almost symplectic manifold, Chaplygin reduction, Nonholonomic Hamiltonian mechanical system, Nonholonomic open-chain multi-body system
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Onboard space systems
Identifiers
URN: urn:nbn:se:ltu:diva-11246DOI: 10.1016/j.mechmachtheory.2014.07.012Scopus ID: 2-s2.0-84908390235Local ID: a2ca9a0a-151b-4e41-a2a8-eab80de2b59bOAI: oai:DiVA.org:ltu-11246DiVA, id: diva2:984195
Note

Uppr├Ąttat; 2014; 20150205 (ninhul)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2019-08-19Bibliographically approved

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