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Nonsmooth Mechanics

Models, Dynamics and Control

  • Book
  • © 1999

Overview

Authors:
  1. Bernard Brogliato

    1. UMR CNRS 5528, Domaine Universitaire, Saint Martin D’Hères, France

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  • This monograph contains the latest research results in the area of impact problems for rigid bodies
  • It contains a complete overview of the main problems of interest in this field
  • This edition has been expanded to include new references and examples

Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Distributional model of impacts

    • Bernard Brogliato
    Pages 1-52

  3. Approximating problems

    • Bernard Brogliato
    Pages 53-75

  4. Variational principles

    • Bernard Brogliato
    Pages 77-103

  5. Two bodies colliding

    • Bernard Brogliato
    Pages 105-171

  6. Multiconstraint nonsmooth dynamics

    • Bernard Brogliato
    Pages 173-261

  7. Generalized impacts

    • Bernard Brogliato
    Pages 263-332

  8. Stability of nonsmooth dynamical systems

    • Bernard Brogliato
    Pages 333-395

  9. Feedback control

    • Bernard Brogliato
    Pages 397-461

  10. Back Matter

    Pages 463-552
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Keywords

About this book

Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in­ put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop­ erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

Reviews

From reviews for the first edition:

It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.

Mathematical Reviews 1998f (Reviewer: P.D. Panagiotopoulos)

The presentation is excellent in combining rigorous mathematics with a great number of examples ranging from simple mechanical systems to robotic systems allowing the reader to understand the basic concepts.

Mathematical Abstracts (Reviewer: H. Troger)

Authors and Affiliations

  • UMR CNRS 5528, Domaine Universitaire, Saint Martin D’Hères, France

    Bernard Brogliato

About the author

In addition to having served (1991 – 2001) as Chargé de Recherche at CNRS, and as, now, Directeur de Recherche at INRIA, Bernard Brogliato is an Associate Editor for Automatica (since 2001) a reviewer for Mathematical Reviews and writes book reviews for ASME Applied Mechanics Reviews. He has served on the organising and other committees of various European and international conferences sponsored by an assortment of organizations, most prominently, the IEEE. He has been responsible for examining the PhD and Habilitation theses of 16 students and takes an active part in lecturing at summer schools in several European countries. Doctor Brogliato is the director of SICONOS (a European project concerned with Modelling, Simulation and Control of Nonsmooth Dynamical Systems) which carries funding of €2 million.

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