Variational nonsmooth mechanics via a projected Hamilton's principle

David Pekarek; Todd D. Murphey

doi:10.1109/acc.2012.6315587

Variational nonsmooth mechanics via a projected Hamilton's principle

David Pekarek^*, Todd D. Murphey

^*Corresponding author for this work

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

This paper presents a projection-based variational formulation of nonsmooth mechanics. In contrast to existing approaches, nonsmooth behavior is captured through the use of a projection mapping on the configuration space. After clearly defining a projected Hamilton's principle, our main focus is on the existence of admissible projection mappings and variational solutions. This lays the foundation necessary for a variety of useful future developments, which includes optimization techniques, stochastic nonsmooth mechanical system models, and integrator symplecticity proofs.

Original language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1040-1046
Number of pages	7
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315587
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2012.6315587

Cite this

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Pekarek, D & Murphey, TD 2012, Variational nonsmooth mechanics via a projected Hamilton's principle. in 2012 American Control Conference, ACC 2012., 6315587, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1040-1046, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6315587

Variational nonsmooth mechanics via a projected Hamilton's principle. / Pekarek, David; Murphey, Todd D.

2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 1040-1046 6315587 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - This paper presents a projection-based variational formulation of nonsmooth mechanics. In contrast to existing approaches, nonsmooth behavior is captured through the use of a projection mapping on the configuration space. After clearly defining a projected Hamilton's principle, our main focus is on the existence of admissible projection mappings and variational solutions. This lays the foundation necessary for a variety of useful future developments, which includes optimization techniques, stochastic nonsmooth mechanical system models, and integrator symplecticity proofs.

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Variational nonsmooth mechanics via a projected Hamilton's principle

Abstract

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