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Nonsmooth Mechanics and Analysis

Theoretical and Numerical Advances

  • Conference proceedings
  • © 2006

Overview

Editors:
  1. P. Alart

    1. Université Montpellier II, Montpellier, France

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  2. O. Maisonneuve

    1. Université Montpellier II, Montpellier, France

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  3. R. T. Rockafellar

    1. University of Washington, Seattle, USA

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  • Illustrates links between developments in nonsmooth analysis and nonsmooth mechanics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 12)

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Table of contents (25 papers)

  1. Multibody Dynamics: Numerical Aspects

    1. The Geometry Of Newton’s Cradle

      • Christoph Glocker, Ueli Aeberhard
      Pages 185-194

    2. Using Nonsmooth Analysis for Numerical Simulation of Contact Mechanics

      • Pierre Alart, David Dureisseix, Mathieu Renouf
      Pages 195-207

    3. Numerical Simulation of a Multibody Gas

      • Michel Jean
      Pages 209-220

    4. Granular Media and Ballasted Railway Tracks Milieux Granulaires Et Voies Ballastées

      • Catherine Cholet, Gilles Saussine, Pierre-Etienne Gautier, Louis-Marie Cléon
      Pages 221-232

    5. Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows

      • Farhang Radjaï, Stéphane Roux
      Pages 233-245

  2. Topics in Nonsmooth Science

    1. Front Matter

      Pages 247-247
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    2. Morphological Equations and Sweeping Processes

      • Jean-Pierre Aubin, José Alberto Murillo Hernández
      Pages 249-259

    3. Higher Order Moreau’s Sweeping Process

      • Vincent Acary, Bernard Brogliato
      Pages 261-277

    4. An Existence Result in Non-Smooth Dynamics

      • Manuel D. P. Monteiro Marques, Laetitia Paoli
      Pages 279-288

    5. Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction

      • Samir Adly, Hedy Attouch, Alexandre Cabot
      Pages 289-304

    6. Canonical Duality in Nonsmooth, Constrained Concave Minimization

      • David Y. Gao
      Pages 305-314

  3. Back Matter

    Pages 315-320
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Keywords

About this book

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

Editors and Affiliations

  • Université Montpellier II, Montpellier, France

    P. Alart, O. Maisonneuve

  • University of Washington, Seattle, USA

    R. T. Rockafellar

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