Stability and Convergence of Mechanical Systems with Unilateral Constraints

  • Remco I. Leine
  • Nathan van de Wouw

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 36)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Remco I. Leine, Nathan van de Wouw
    Pages 1-19
  3. Remco I. Leine, Nathan van de Wouw
    Pages 21-41
  4. Remco I. Leine, Nathan van de Wouw
    Pages 43-57
  5. Remco I. Leine, Nathan van de Wouw
    Pages 59-77
  6. Remco I. Leine, Nathan van de Wouw
    Pages 79-107
  7. Remco I. Leine, Nathan van de Wouw
    Pages 109-152
  8. Remco I. Leine, Nathan van de Wouw
    Pages 153-190
  9. Remco I. Leine, Nathan van de Wouw
    Pages 191-215
  10. Remco I. Leine, Nathan van de Wouw
    Pages 217-219
  11. Back Matter
    Pages 223-236

About this book

Introduction

Stability of motion is a central theme in the dynamics of mechanical systems. 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 starts with the treatise of the mathematical background on non-smooth analysis, measure and integration theory and an introduction to the field of non-smooth dynamical systems. The unilateral constraints are modelled in the framework of set-valued force laws developed in the field of non-smooth mechanics. The embedding of these constitutive models in the dynamics of mechanical systems gives rises to dynamical models with impulsive phenomena. This book uses the mathematical framework of measure differential inclusions to formalise such models. The book proceeds with the presentation of stability results for measure differential inclusions.

These stability results are then applied to nonlinear mechanical systems with unilateral constraints. The book closes with the study of the convergence property for a class of measure differential inclusions; a stability property for systems with time-varying inputs which is shown to be highly instrumental in the context of the control of mechanical systems with unilateral constraints.

While the book presents a profound stability theory for mechanical systems with unilateral constraints, it also has a tutorial value on the modelling of such systems in the framework of measure differential inclusions. The work will be of interest to engineers, scientists and

students working in the field of non-smooth mechanics and dynamics.

Keywords

Convergence Mechanical Systems Non-Smooth Systems Stability Unilateral Constraints calculus dynamische Systeme friction mechanics modeling

Editors and affiliations

  • Remco I. Leine
    • 1
  • Nathan van de Wouw
    • 2
  1. 1.Department of Mechanical and Process EngineeringInstitute of Mechanical SystemsETH ZurichSwitzerland
  2. 2.Dynamics and Control Group Department of Mechanical EngineeringEindhoven University of Technology5600 MB EindhovenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-76975-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-76974-3
  • Online ISBN 978-3-540-76975-0
  • Series Print ISSN 1613-7736
  • About this book