Dynamics of an impact oscillator near a degenerate graze

Description/Abstract

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 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.