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Existence of Periodic Orbits with Zeno Behavior in Completed Lagrangian Hybrid Systems

Or, Yizhar and Ames, Aaron D. (2009) Existence of Periodic Orbits with Zeno Behavior in Completed Lagrangian Hybrid Systems. In: Hybrid Systems: Computation and Control 2009. Lecture Notes in Computer Science. Vol.5469. No.5469. Springer , pp. 291-305. ISBN 978-3-642-00601-2 . https://resolver.caltech.edu/CaltechAUTHORS:20100614-134937637

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Abstract

In this paper, we consider hybrid models of mechanical systems undergoing impacts, Lagrangian hybrid systems, and study their periodic orbits in the presence of Zeno behavior-an infinite number of impacts occurring in finite time. The main result of this paper is explicit conditions under which the existence of stable periodic orbits for a Lagrangian hybrid system with perfectly plastic impacts implies the existence of periodic orbits in the same system with non-plastic impacts. Such periodic orbits contain phases of constrained and unconstrained motion, and the transition between them necessarily involves Zeno behavior. The result is practically useful for a wide range of unilaterally constrained mechanical systems under cyclic motion, as demonstrated through the example of a double pendulum with a mechanical stop.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-3-642-00602-9_21DOIArticle
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2009 Springer-Verlag Berlin Heidelberg.
Series Name:Lecture Notes in Computer Science
Issue or Number:5469
Record Number:CaltechAUTHORS:20100614-134937637
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100614-134937637
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18668
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jul 2010 22:08
Last Modified:03 Oct 2019 01:46

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