Multiple instantaneous collisions in a variational framework

Vlad Seghete; Todd David Murphey

doi:10.1109/CDC.2009.5400369

Multiple instantaneous collisions in a variational framework

Vlad Seghete^*, Todd David Murphey

^*Corresponding author for this work

Mechanical Engineering

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

5 Scopus citations

Abstract

Variational integrators have become of interest to the controls community, particularly since in recent years they have been used in the context of optimal control. This paper discusses how to resolve simultaneous impacts in a variational context, assuming that all boundaries of the impacting bodies are differentiable. We demonstrate how this analysis works for arbitrary numbers of simultaneous impacts and derive discrete time algorithms for resolving these impacts numerically. We illustrate our results, both in the continuous and discrete domain, using Newton's cradle as an example.

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages	5015-5020
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2009.5400369
State	Published - Dec 1 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5400369

Cite this

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title = "Multiple instantaneous collisions in a variational framework",

abstract = "Variational integrators have become of interest to the controls community, particularly since in recent years they have been used in the context of optimal control. This paper discusses how to resolve simultaneous impacts in a variational context, assuming that all boundaries of the impacting bodies are differentiable. We demonstrate how this analysis works for arbitrary numbers of simultaneous impacts and derive discrete time algorithms for resolving these impacts numerically. We illustrate our results, both in the continuous and discrete domain, using Newton's cradle as an example.",

author = "Vlad Seghete and Murphey, {Todd David}",

year = "2009",

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doi = "10.1109/CDC.2009.5400369",

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booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Seghete, V & Murphey, TD 2009, Multiple instantaneous collisions in a variational framework. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400369, Proceedings of the IEEE Conference on Decision and Control, pp. 5015-5020, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5400369

Multiple instantaneous collisions in a variational framework. / Seghete, Vlad; Murphey, Todd David.

Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. p. 5015-5020 5400369 (Proceedings of the IEEE Conference on Decision and Control).

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

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N2 - Variational integrators have become of interest to the controls community, particularly since in recent years they have been used in the context of optimal control. This paper discusses how to resolve simultaneous impacts in a variational context, assuming that all boundaries of the impacting bodies are differentiable. We demonstrate how this analysis works for arbitrary numbers of simultaneous impacts and derive discrete time algorithms for resolving these impacts numerically. We illustrate our results, both in the continuous and discrete domain, using Newton's cradle as an example.

AB - Variational integrators have become of interest to the controls community, particularly since in recent years they have been used in the context of optimal control. This paper discusses how to resolve simultaneous impacts in a variational context, assuming that all boundaries of the impacting bodies are differentiable. We demonstrate how this analysis works for arbitrary numbers of simultaneous impacts and derive discrete time algorithms for resolving these impacts numerically. We illustrate our results, both in the continuous and discrete domain, using Newton's cradle as an example.

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Multiple instantaneous collisions in a variational framework

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