Multiple instantaneous collisions in a variational framework

Vlad Seghete; Todd D. Murphey

doi:10.1109/CDC.2009.5400369

Multiple instantaneous collisions in a variational framework

Vlad Seghete^*, Todd D. 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
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5015-5020
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400369
State	Published - 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)	0743-1546
ISSN (Electronic)	2576-2370

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

Seghete, V., & Murphey, T. D. (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 (pp. 5015-5020). Article 5400369 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400369

@inproceedings{63d0e2863a614a958246a2a0fc1210e9,

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 D.\}",

year = "2009",

doi = "10.1109/CDC.2009.5400369",

language = "English (US)",

isbn = "9781424438716",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5015--5020",

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

address = "United States",

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",

}

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

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

TY - GEN

T1 - Multiple instantaneous collisions in a variational framework

AU - Seghete, Vlad

AU - Murphey, Todd D.

PY - 2009

Y1 - 2009

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.

UR - http://www.scopus.com/inward/record.url?scp=77950790748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950790748&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5400369

DO - 10.1109/CDC.2009.5400369

M3 - Conference contribution

AN - SCOPUS:77950790748

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5015

EP - 5020

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

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

Y2 - 15 December 2009 through 18 December 2009

ER -

Seghete V, Murphey TD. 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. Institute of Electrical and Electronics Engineers Inc. 2009. p. 5015-5020. 5400369. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400369

Multiple instantaneous collisions in a variational framework

Abstract

Publication series

Other

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this