Nonsmooth Mechanics: Models, Dynamics and Control by Bernard Brogliato (English)

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The Nile on eBay FREE SHIPPING UK WIDE Nonsmooth Mechanics by Bernard Brogliato 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 (-, . 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Notes 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 Back Cover This significantly enlarged and expanded second edition focuses on a class of nonsmooth hybrid dynamical systems, namely finite-dimensional mechanical systems subject to unilateral constraints. It contains a complete overview of the main problems in mathematics, mechanics, stability and control which are of interest in this field. The following topics are discussed in detail and are illustrated with examples: * shock dynamics; * multiple impacts; * feedback control; * Moreau's sweeping process; and * complementarity formulations. With a comprehensive bibliography of over a thousand references, Nonsmooth Dynamics is an indispensable source of information on impact phenomena and rigid-body dynamics. Praise for the first edition: 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 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 Table of Contents 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. Review 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) Promotional Springer Book Archives Long Description 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 Review Quote 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) Feature 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 Details ISBN 1447111613 Author Bernard Brogliato Language English Subtitle Models, Dynamics and Control Year 2012 Media Book Birth 1963 Imprint Springer London Ltd Place of Publication England Country of Publication United Kingdom Short Title NONSMOOTH MECHANICS 1999 SOFTC Replaces 9783540760795 UK Release Date 2012-10-05 AU Release Date 2012-10-05 NZ Release Date 2012-10-05 Illustrations XX, 552 p. Pages 552 Publisher Springer London Ltd ISBN-10 1447111613 ISBN-13 9781447111610 Publication Date 2012-10-05 Series Communications and Control Engineering Edition 2nd Format Paperback Alternative 9781852331436 DEWEY 620.1054 Audience Professional & Vocational Replaced by 9783319286624 Country of Origin NL Product Class Description Mechanical Engineering Edition Description Second Edition 1999 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! 30 DAY RETURN POLICY No questions asked, 30 day returns! FREE DELIVERY No matter where you are in the UK, delivery is free. SECURE PAYMENT Peace of mind by paying through PayPal and eBay Buyer Protection TheNile_Item_ID:137808889;