Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete
System with Unilateral Contact and Coulomb Friction explores the
effects of small and large deformations to understand how shocks,
sliding, and stick phases affect the trajectories of mechanical
systems. By analyzing these non-regularities successively this work
explores the set of equilibria and properties of periodic solutions
of elementary mechanical systems, where no classical results issued
from the theory of ordinary differential equations are readily
available, such as stability, continuation or approximation of
solutions. The authors focus on unilateral contact in presence of
Coulomb friction and show, in particular, how any regularization
would greatly simplify the mathematics but lead to unacceptable
physical responses.
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