Nonsmooth Mechanics

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and NewtonEuler 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 detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems.
Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first centuryincluding developments in:

• the existence and uniqueness of solutions;

• impact models;

• extension of the LagrangeDirichlet theorem and trajectory tracking; and

• well-posedness of contact complementarity problems with and without friction.

  Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices.
  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

  Enriches your knowledge of all aspects of nonsmooth mechanics: mathematics; modelling; control; and stability Substantially rewritten, edited and updated, the new edition brings a classic reference right up to date Extensive bibliography of 1,100 entries is convenient for researchers Broadens your understanding of nonsmooth dynamical systems in general by providing links with impulsive ODEs, hybrid systems and electrical circuits Summarizes the latest studies on impact models Uses many detailed examples and figures to illustrate the main theoretical developments Includes supplementary material: sn.pub/extras

  Autorentext
  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.

  Inhalt
  Impulsive Dynamics and Measure Differential Equations.- Visco-Elastic Contact/Impact Models.- Variational Principles.- Two-Body Collisions and Restitution Rules. Lagrangian Complementarity Systems.- Generalized and Multiple Impacts.- Lyapunov Stability.- Trajectory Tracking.- Appendices: Schwartz Distributions; Measures and Integrals; Functions of Bounded Variation in Time. Elements of Convex Analysis.