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Introduction to Flow Passability

In: Discontinuous Dynamical Systems

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  • Albert C. J. Luo

    (Southern Illinois University Edwardsville, Department of Mechanical and Industrial Engineering)

Abstract

In this Chapter, the passability of a flow to the boundary of two different dynamical systems will be presented. The accessible and inaccessible sub-domains will be introduced first for a theory of discontinuous dynamic systems. On the accessible domains, the corresponding dynamic systems will be introduced. The flow orientation and singular sets of boundary will be discussed. The passability and tangency (grazing) of a flow to the separation boundary between two adjacent accessible domains will be presented, and the necessary and sufficient conditions for such passability and tangency of the flow to the boundary will be presented. An L-function of flows will be introduced, and the switching bifurcation conditions for the flow passability to the boundary will be discussed. Finally, a frictioninduced oscillator will be presented as an example.

Suggested Citation

  • Albert C. J. Luo, 2012. "Introduction to Flow Passability," Springer Books, in: Discontinuous Dynamical Systems, chapter 0, pages 9-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-22461-4_2
    DOI: 10.1007/978-3-642-22461-4_2
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