Nonholonomic Mechanics and Control

The goal of this book is to explore some of the connections between control theory and geometric mechanics; that is, control theory is linked with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems subject to motion constraints. The synthesis of the topic is appropriate as there is a particularly rich connection between mechanics and nonlinear control theory. The aim is to provide a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material that has not yet made its way into texts and monographs. This book is intended for graduate students who wish to learn this subject and researchers in the area who want to enhance their techniques.

List of contents

Preface About the Authors A Diagram for the Book Introduction Mathematical Preliminaries Basic Concepts in Geometric Mechanics Introduction to Aspects of Geometric Control Theory Nonholonomic Mechanics Control of Mechanical and Nonholonomic Systems Optimal Control Stability of Nonholonomic Systems Energy-Based Methods for Stabilitization References Index

Report

From the reviews:"As aptly formulated in its preface, Nonholonomic Mechanics and Control links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular, with the theory of mechanical systems subject to kinematic motion constraints. The analysis and control of mechanical systems has been an active research area over the last several decades. This book aims to present some of this material, often scattered throughout the literature, in a cohesive manner. ... Although, unavoidably, the opening chapters provide only a 'crash course' at some points, the material has been written with much care. In fact, in many cases, the clarity of the presentation is unmatched elsewhere in the literature. ... This book is a welcome addition to the existing literature and will certainly become a standard reference. ... It is to be expected that Bloch's book will be a continuing source of inspiration for further research in this area. ... In summary, this is a delightful book that will be valuable for both the control community and researchers working on the geometric theory of mechanical systems. With its extensive illustrations and exercises, this book is eminently suited for a graduate course. The author should be congratulated for such an admirable job." (A.J. van der Schaft, IEEE Control Systems Magazine, June 2005)"... A well-written and comprehensive reference that can be used as a graduate-level textbook, complete with exercises. The book also gives a nice history of the development of the methods covered, and it is an excellent resource for references for further reading. ... The book's background material in differential geometry, mechanics, and geometric control gives the book a timeless feel, while the extensive coverage of recent research results conveys the vitality of the field. This book will make an excellent reference for students and researchers in differential geometric control. It will also make a fine textbook for engineering graduate students with a background in differential geometry. For graduate students with a more traditional engineering mathematics background, portions of this book can be coupled with supplementary reading and example-based introduction of the relevant mathematical concepts." ( IEEE Transactions on Automatic Control )"Nonholonomic Mechanics and Control links control theory with a geometric view of classical mechanics ... . This book is a welcome addition to the existing literature and will certainly become a standard reference. ... Bloch's book will be a continuing source of inspiration for further research in this area. ... this is a delightful book that will be valuable for both the control community and researchers ... . is eminently suited for a graduate course. The author should be congratulated for such an admirable job." (A.J. van der Schaft, IEEE Control System Magazine, June, 2005)"The book ... aims to explore connections between control theory and geometric mechanics. ... This book can be considered as a mixture between a research monograph and a textbook, as a lot of exercises ... are given. ... contains an exhaustive list of contemporary references. ... After reading this book the reader will be convinced that the aim of the book ... is successfully reached. ... it is a nice and useful learning tool for scientists and engineers from academia and industry." (Clementina Mladenova, Zentralblatt MATH, Vol. 1045 (20), 2004)"The aim of this book is 'to provide a unified treatment of nonlinear control theory and constrained mechanical systems that will incorporate material that has not yet made its way into texts and monographs'. ... the authors of the present book have contributed a great deal to the way in which nonholonomic systems are currently understood ... . The book constitutes an accurate reflection of this work, and covers a broad variety of topics and problems concerning nonholonomic systems and contro

Product details

• Authors: A M Bloch, A. M. Bloch, Anthony Bloch
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2003
• EAN: 9780387955353
• ISBN: 978-0-387-95535-3
• No. of pages: 484
• Weight: 814 g
• Illustrations: 40 SW-Abb.
• Series: Interdisciplinary Applied Mathematics; Interdisciplinary Applied Mathematics
• Subject: Natural sciences, medicine, IT, technology > Physics, astronomy > Mechanics, acoustics