Dynamics of an impact oscillator near a degenerate graze

Details Dynamics of an impact oscillator near a degenerate graze Dynamics of an impact oscillator near a degenerate graze

2010-05-18

arxiv.org/abs/1005.3286v1

Nonlinear Sciences

Chaotic Dynamics

32 pages, 17 figures

Scientific paper

We give a complete analysis of low-velocity dynamics close to grazing for a generic one degree of freedom impact oscillator. This includes nondegenerate (quadratic) grazing and minimally degenerate (cubic) grazing, corresponding respectively to nondegenerate and degenerate {\em chatter}. We also describe the dynamics associated with generic one-parameter bifurcation at a more degenerate (quartic) graze, showing in particular how this gives rise to the often-observed highly convoluted structure in the stable manifolds of chattering orbits. The approach adopted is geometric, using methods from singularity theory.

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