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HYBRID
2009
Springer

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

10 years 2 months ago
Existence of Periodic Orbits with Zeno Behavior in Completed Lagrangian Hybrid Systems
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, where an infinite sequence of impacts converges 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.
Yizhar Or, Aaron D. Ames
Added 19 May 2010
Updated 19 May 2010
Type Conference
Year 2009
Where HYBRID
Authors Yizhar Or, Aaron D. Ames
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