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Updated: Jul 3, 2026

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
Published on: August 5, 2016
Invariant polygons in systems with grazing-sliding
1Bristol Centre for Applied Nonlinear Mathematics, University of Bristol, University Walk, Bristol, BS8 1TR, United Kingdom. r.szalai@bristol.ac.uk
Abstract:
The paper investigates generic three-dimensional nonsmooth 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 system has an attractor that consists 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 must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.
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