Nonsmooth Mechanics

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.

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)

• 1 Distributional model of impacts.- 1.1 External percussions.- 1.2 Measure differential equations.- 1.3 Systems subject to unilateral constraints.- 1.4 Changes of coordinates in MDEs.- 2 Approximating problems.- 2.1 Simple examples.- 2.2 The method of penalizing functions.- 3 Variational principles.- 3.1 Virtual displacements principle.- 3.2 Gauss’ principle.- 3.3 Lagrange’s equations.- 3.4 External impulsive forces.- 3.5 Hamilton’s principle and unilateral constraints.- 4 Two bodies colliding.- 4.1 Dynamical equations of two rigid bodies colliding.- 4.2 Percussion laws.- 5 Multiconstraint nonsmooth dynamics.- 5.1 Introduction. Delassus’ problem.- 5.2 Multiple impacts: the striking balls examples.- 5.3 Moreau’s sweeping process.- 5.4 Complementarity formulations.- 5.5 The Painlevé’s example.- 5.6 Numerical analysis.- 6 Generalized impacts.- 6.1 The frictionless case.- 6.2 The use of the kinetic metric.- 6.3 Simple generalized impacts.- 6.4 Multiple generalized impacts.- 6.5 General restitution rules for multiple impacts.- 6.6 Constraints with Amontons-Coulomb friction.- 6.7 Additional comments and studies.- 7 Stability of nonsmooth dynamical systems.- 7.1 General stability concepts.- 7.2 Grazing orC-bifurcations.- 7.3 Stability: from compliant to rigid models.- 8 Feedback control.- 8.1 Controllability properties.- 8.2 Control of complete robotic tasks.- 8.3 Dynamic model.- 8.4 Stability analysis framework.- 8.5 A one degree-of-freedom example.- 8.6ndegree-of-freedom rigid manipulators.- 8.7 Complementary-slackness juggling systems.- 8.8 Systems with dynamic backlash.- 8.9 Bipedal locomotion.- A Schwartz’ distributions.- A.1 The functional approach.- A.2 The sequential approach.- A.3 Notions of convergence.- B Measures and integrals.- C Functions ofbounded variation in time.- C.1 Definition and generalities.- C.2 Spaces of functions of bounded variation.- C.3 Sobolev spaces.- D Elements of convex analysis.