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Qualitative Analysis of Nonsmooth Dynamics

A Simple Discrete System with Unilateral Contact and Coulomb Friction

Alain Léger, CNRS, Marseille, France Elaine Pratt, Aix-Marseille University, France

ISBN: 9781785480942

Publication Date: April 2016   Hardback   222 pp.

130.00 USD

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This book investigates the behavior of simple nonsmooth mechanical systems where the nonsmoothness arises from non-regularized unilateral contact and Coulomb friction.
The authors focus on Coulomb friction to discuss how regularization greatly simplifies the mathematics behind this dynamics but may remove the main qualitative features and thus lead to non-physical properties. The book explores the effects of the non-regularities and shows that the trajectories of mechanical systems include shocks, sliding and stick phases.
The authors draw from their own research as well as from studies in the wider field of solid mechanics to present their book in the context of the mechanics of discrete systems.


1. The Model.
2. Mathematical Formulation.
3. The Equilibrium States.
4. Stability.
5. Exploring the Case of the Linear Restoring Force.
6. The Case of the Nonlinear Restoring Force.
7. Open Problems and Challenges.

About the Authors

Alain Léger is a researcher at the Mechanics and Acoustics Laboratory at CNRS in Marseille, France.
Elaine Pratt is a researcher at Aix-Marseille University in Marseille, France.


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