Nonsmooth Mechanics

Models, Dynamics and Control

  • Bernard Brogliato

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Bernard Brogliato
    Pages 51-93
  3. Bernard Brogliato
    Pages 95-125
  4. Bernard Brogliato
    Pages 127-240
  5. Bernard Brogliato
    Pages 241-370
  6. Bernard Brogliato
    Pages 371-415
  7. Bernard Brogliato
    Pages 417-476
  8. Bernard Brogliato
    Pages 477-534
  9. Bernard Brogliato
    Pages E1-E11
  10. Back Matter
    Pages 535-628

About this book


Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given in-depth exposition connected by a framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements and with other nonsmooth dynamical systems like impulsive and piecewise linear systems.

Nonsmooth Mechanics (third edition) has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction.

With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics.

The book’s two best features, in my view are its detailed survey of the literature… and its detailed presentation of many examples illustrating both the techniques and their limitations… For readers interested in the field, this book will serve as an excellent introductory survey.

Andrew Lewis in Automatica

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.

Panagiotis D. Panagiotopoulos in Mathematical Reviews

The presentation is excellent in combining rigorous mathematics with a great number of examples… allowing the reader to understand the basic concepts.

Hans Troger in Mathematical Abstracts


Complementarity Problems and Systems Convex Analysis and Complementarity Theory Hybrid Dynamical Systems Impact and Contact Mechanics Impulsive Systems Mechanical Systems with Constraints Moreau’s Sweeping Process and Variational Inequalities Multibody Multicontact Mechanical Systems Stability and Control of Non-smooth Lagrangian Systems Unilateral & Bilateral Constraints with or without Coulomb’s Friction

Authors and affiliations

  • Bernard Brogliato
    • 1
  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-28662-4
  • Online ISBN 978-3-319-28664-8
  • Series Print ISSN 0178-5354
  • Series Online ISSN 2197-7119
  • Buy this book on publisher's site