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Invariant polygons in systems with grazing-sliding

Research output: Working paperWorking paper and Preprints

Original languageEnglish
StatePublished - 7 Aug 2007


We investigate generic three-dimensional non-smooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the attractor of the system will consist of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor resides on a polygonal-shaped invariant set and classify the number of sides as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.

Additional information

Sponsorship: The research of R.S. was supported by grant EP/C544048/1 of the Engineering and Physical Sciences Research Council (EPSRC). The research of H.M.O. was supported by an EPSRC Advanced Research Fellowship.

Research areas

  • Filippov-system, normal form

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  • Preprint

    Submitted manuscript, 1 MB, PDF-document


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