|State||Published - 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.
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.
- Filippov-system, normal form