Dynamics of an impact oscillator near a degenerate graze

2010/05/18 by D. R. J. Chillingworth, D R J Chillingworth, Chillingworth, D R J
Engineering · Mathematics · Physics and Astronomy · #34A36 #34C23 #37B55 #70G60 #70K40 #70K50 #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems #math.DS #msc:34A36 #msc:34C23 #msc:37B55 #msc:70G60 #msc:70K40 #msc:70K50 #nlin.CD

paper · pdf · doi:10.48550/arxiv.1005.3286

32 pages, 17 figures

arxiv created 2010/05/18 · openalex publication_date 2010/05/18 · arxiv updated 2010/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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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