Stability and Convergence of Mechanical Systems with Unilateral Constraints (eBook)

Remco I. Leine, Nathan van de Wouw (Autoren)

eBook Download: PDF

2007
XIV, 236 Seiten
Springer Berlin (Verlag)
978-3-540-76975-0 (ISBN)

Infos

While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.

Inhalt

Preface 6
Contents 8
Notation 11
1 Introduction 14
1.1 Motivation 14
1.2 Historical Notes on the Theory of Stability 16
1.3 Non-smooth Dynamical Systems 21
1.4 Stability and Convergence 24
1.5 Literature Survey 26
1.6 Objective and Scope 30
1.7 Outline 31
2 Non-smooth Analysis 33
2.1 Sets 33
2.2 Functions and Continuity 35
2.3 Generalised Derivatives 38
2.4 Set-valued Functions 40
2.5 De.nitions from Convex Analysis 45
2.6 Subderivative 51
2.7 Summary 52
3 Measure and Integration Theory 54
3.1 Measures 54
3.2 The Lebesgue Integral 56
3.3 Signed Measures 57
3.4 Real Measures 60
3.5 Di.erential Measures 63
3.6 The Differential Measure of a Bilinear Form 66
3.7 Summary 68
4 Non-smooth Dynamical Systems 69
4.1 Differential Equations 69
4.2 Differential Inclusions 70
4.3 Measure Differential Inclusions 78
4.4 Summary 86
5 Mechanical Systems with Set-valued Force Laws 88
5.1 Non-smooth Potential Theory 88
5.2 Contact Geometry 92
5.3 Force Laws for Frictional Unilateral Contact 93
5.4 Measure Newton-Euler Equations 108
5.5 Summary 115
6 Lyapunov Stability Theory for Measure Differential Inclusions 117
6.1 Mathematical Preliminaries 118
6.2 Invariant Sets and Limit Sets 122
6.3 Definitions of Stability Properties for Autonomous Systems 127
6.4 Definitions of Stability Properties of Solutions Non-autonomous Systems 130
6.5 Basic Lyapunov Theorems of Autonomous Systems 134
6.6 LaSalle’s Invariance Principle 153
6.7 Instability 155
6.8 Summary 159
7 Stability Properties in Mechanical Systems 161
7.1 Total Mechanical Energy 161
7.2 Stability Results for Mechanical Systems 170
7.3 Attractivity of Equilibrium Sets 176
7.4 Instability of Equilibrium Positions and Sets 182
7.5 Examples 186
7.6 Summary 198
8 Convergence Properties of Monotone Measure Di.erential Inclusions 199
8.1 Convergent Systems 199
8.2 Convergence of Maximal Monotone Systems 201
8.3 Tracking Control for Lur’e Type Systems 207
8.4 Illustrative Examples 210
8.5 Summary 222
9 Concluding Remarks 224
Sources and Translations 227
References 228
Index 238

Produkt-Details

• Erscheint lt. Verlag: 29.12.2007
• Reihe/Serie: Lecture Notes in Applied and Computational Mechanics
• Reihe/Serie: Lecture Notes in Applied and Computational Mechanics
• Zusatzinfo: XIV, 236 p. 56 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Calculus • convergence • Dynamische Systeme • Friction • Mechanical Systems • Mechanics • Modeling • Non-smooth Systems • stability • Unilateral Constraints
• ISBN-10: 3-540-76975-7 / 3540769757
• ISBN-13: 978-3-540-76975-0 / 9783540769750