© 2016

Nonsmooth Mechanics

Models, Dynamics and Control


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

  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

About the authors

Bernard Brogliato is Senior Researcher at INRIA Grenoble, France, where he founded and leads the team BIPOP. He published more than 70 journal articles in the fields of systems and Control, Solid Mechanics, and Applied Mathematics, as well as 5 monographs. His research interests are in non-smooth dynamical systems (mechanical systems with constraints, impacts, friction, electrical circuits with non-smooth components, sliding-mode control, optimal control with state constraints), and dissipative systems. He was an Associate Editor for Automatica, and the chairman of two Euromech Colloquia dedicated to Impact Mechanics. He coordinated the FP5 European project SICONOS (2 million euros fundings, 13 partners), and two projects funded by the French National Agency for Scientific Research, on multiple impacts and discrete-time sliding mode control.

Bibliographic information

  • Book Title Nonsmooth Mechanics
  • Book Subtitle Models, Dynamics and Control
  • Authors Bernard Brogliato
  • Series Title Communications and Control Engineering
  • Series Abbreviated Title Communicat., Control Engineering
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-28662-4
  • Softcover ISBN 978-3-319-80401-9
  • eBook ISBN 978-3-319-28664-8
  • Series ISSN 0178-5354
  • Series E-ISSN 2197-7119
  • Edition Number 3
  • Number of Pages XXI, 628
  • Number of Illustrations 0 b/w illustrations, 107 illustrations in colour
  • Additional Information Originally published in 1996 as volume 220 in the series: Lecture Notes in Control and Information Sciences
  • Topics Control and Systems Theory
    Nanotechnology and Microengineering
    Vibration, Dynamical Systems, Control
    Systems Theory, Control
  • Buy this book on publisher's site
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