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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
Inhaltsverzeichnis
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.
Produktdetails
Erscheinungsdatum
06. Dezember 2012
Sprache
englisch
Auflage
2nd ed. 1999
Seitenanzahl
552
Dateigröße
81,39 MB
Reihe
Communications and Control Engineering
Autor/Autorin
Bernard Brogliato
Verlag/Hersteller
Kopierschutz
mit Wasserzeichen versehen
Produktart
EBOOK
Dateiformat
PDF
ISBN
9781447105572
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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)
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