Non-Smooth Deterministic or Stochastic Discrete Dynamical Systems (PDF)

This book contains theoretical and application-oriented methods
to treat models of dynamical systems involving non-smooth
nonlinearities.

The theoretical approach that has been retained and underlined in
this work is associated with differential inclusions of mainly
finite dimensional dynamical systems and the introduction of
maximal monotone operators (graphs) in order to describe models of
impact or friction. The authors of this book master the
mathematical, numerical and modeling tools in a particular way so
that they can propose all aspects of the approach, in both a
deterministic and stochastic context, in order to describe real
stresses exerted on physical systems. Such tools are very powerful
for providing reference numerical approximations of the models.
Such an approach is still not very popular nevertheless, even
though it could be very useful for many models of numerous fields
(e.g. mechanics, vibrations, etc.).

This book is especially suited for people both in research and
industry interested in the modeling and numerical simulation of
discrete mechanical systems with friction or impact phenomena
occurring in the presence of classical (linear elastic) or
non-classical constitutive laws (delay, memory effects, etc.). It
aims to close the gap between highly specialized mathematical
literature and engineering applications, as well as to also give
tools in the framework of non-smooth stochastic differential
systems: thus, applications involving stochastic excitations
(earthquakes, road surfaces, wind models etc.) are considered.

Contents

1. Some Simple Examples.

2. Theoretical Deterministic Context.

3. Stochastic Theoretical Context.

4. Riemannian Theoretical Context.

5. Systems with Friction.

6. Impact Systems.

7. Applications-Extensions.

About the Authors

Jérôme Bastien is Assistant Professor at the
University Lyon 1 (Centre de recherche et d'Innovation sur le
sport) in France.

Frédéric Bernardin is a Research Engineer at
Département Laboratoire de Clermont-Ferrand (DLCF), Centre
d'Etudes Techniques de l'Equipement (CETE), Lyon, France.

Claude-Henri Lamarque is Head of Laboratoire Géomatériaux
et Génie Civil (LGCB) and Professor at Ecole des Travaux
Publics de l'Etat (ENTPE), Vaulx-en-Velin, France.