Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb...

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Alain Léger (Research Associate, Mechanics and Acoustics Laboratory, CNRS, Marseille, France) Elaine Pratt (Researcher, University Aix-Marseille, Marseille, France)

Qualitative Analysis of Nonsmooth Dynamics

A Simple Discrete System with Unilateral Contact and Coulomb Friction

Alain Léger (Research Associate, Mechanics and Acoustics Laboratory, CNRS, Marseille, France), Elaine Pratt (Researcher, University Aix-Marseille, Marseille, France)

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English

ISTE Press Ltd - Elsevier Inc
04 April 2016

Dynamics & vibration

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.

By: Alain Léger (Research Associate Mechanics and Acoustics Laboratory CNRS Marseille France), Elaine Pratt (Researcher, University Aix-Marseille, Marseille, France)
Imprint: ISTE Press Ltd - Elsevier Inc
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 151mm, Spine: 16mm
Weight: 360g
ISBN: 9781785480942
ISBN 10: 1785480944
Pages: 222
Publication Date: 04 April 2016
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

IntroductionChapter 1. The ModelChapter 2. Mathematical FormulationChapter 3. The Equilibrium StatesChapter 4. StabilityChapter 5. Exploring the Case of the Linear Restoring ForceChapter 6. The Case of the Nonlinear Restoring ForceChapter 7. Open Problems and Challenges

Alain Leger received his PhDs in Mathematics and Sciences from the University Pierre et Marie Curie, Paris. He held positions as research engineer and senior research at EDF and CNRS respectively. He is the co-manager of the International Scientific Coordination Network of 'Wave Propagation in Complex Media'. His research areas lie in the mechanics of solids and structure, unilateral problems within the dynamics of discrete systems, bifurication theory and wave propagation in complex media. Elaine Pratt obtained her PhD in Numerical Analysis in 1979 from the University of Provence. She has held the position of Senior Lecturer at the Univeristy of Provence and the University Aix-Marseille. Her research interests include mathematical and numerical analysis applied to mechanical problems, the study of contact friction and non-smooth dynamics of discrete mechanical systems.

Reviews for Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction

"""The book is likely to be of greatest interest and use to researchers and graduate students working with friction related problems. Indeed, the clarity of the writing is likely to provide inspiration for students and researchers to take the state-of-the-art of the subject matter even further."" --Zentralblatt MATH"