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

Summary: Existence of Periodic Orbits with Zeno Behavior
in Completed Lagrangian Hybrid Systems
Yizhar Or1
and Aaron Ames2
1
Control and Dynamical Systems
California Institute of Technology, Pasadena, CA 91125
izi@cds.caltech.edu
2
Department of Mechanical Engineering
Texas A&M University, College Station, TX
aames@tamu.edu
Abstract. In this paper, we consider hybrid models of mechanical sys-
tems undergoing impacts -- Lagrangian hybrid systems, and study their
periodic orbits in the presence of Zeno behavior, where an infinite se-
quence 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

  

Source: Ames, Aaron - Department of Mechanical Engineering, Texas A&M University

 

Collections: Engineering