Stability and Convergence of Mechanical Systems with Unilateral Constraints

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.

List of contents

Non-smooth Analysis.- Measure and Integration Theory.- Non-smooth Dynamical Systems.- Mechanical Systems with Set-valued Force Laws.- Lyapunov Stability Theory for Measure Differential Inclusions.- Stability Properties in Mechanical Systems.- Convergence Properties of Monotone Measure Differential Inclusions.- Concluding Remarks.

Summary

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.

Additional text

From the reviews:

"The monograph represents results on stability and attractivity obtained recently for continuous-time dynamical systems formulated as measure differential inclusions. … Some illustrative examples of convergent mechanical systems with set-valued force laws are presented. The monograph will be of interest to researches and engineers working in the field of non-smooth dynamics and mechanics." (Boris Ivanovich Konosevich, Zentralblatt MATH, Vol. 1143, 2008)
"This monograph presents a qualitative analysis of non-smooth mechanical systems. … Illustrative examples highlight the use and the limits of the theory. … The monograph is easy to read and the single steps are well motivated and illustrated." (Florian Schmid, Mathematical Reviews, Issue 2009 g)

Report

From the reviews:

"The monograph represents results on stability and attractivity obtained recently for continuous-time dynamical systems formulated as measure differential inclusions. ... Some illustrative examples of convergent mechanical systems with set-valued force laws are presented. The monograph will be of interest to researches and engineers working in the field of non-smooth dynamics and mechanics." (Boris Ivanovich Konosevich, Zentralblatt MATH, Vol. 1143, 2008)
"This monograph presents a qualitative analysis of non-smooth mechanical systems. ... Illustrative examples highlight the use and the limits of the theory. ... The monograph is easy to read and the single steps are well motivated and illustrated." (Florian Schmid, Mathematical Reviews, Issue 2009 g)

Product details

• Authors: Nathan van de Wouw, Remco Leine, Remco I Leine, Remco I. Leine, Nathan van de Wouw, Nathan van de Wouw
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 14.04.2009
• EAN: 9783540769743
• ISBN: 978-3-540-76974-3
• No. of pages: 236
• Dimensions: 155 mm x 17 mm x 235 mm
• Weight: 491 g
• Illustrations: XIV, 236 p. 56 illus.
• Series: Lecture Notes in Applied and Computational Mechanics; Lecture Notes in Applied and Computational Mechanics
• Subject: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering