Overview

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.

Full Product Details

Author:   Remco I. Leine ,  Nathan van de Wouw
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2008
Volume:   36
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642095696

ISBN 10:   3642095690
Pages:   236
Publication Date:   25 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table 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.

Reviews

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)

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)

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)

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)

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