Some Applications of Differential Geometry in Control
Differential geometry has been introduced to control about 25 years ago. This contribution shows, how one can identify dynamic systems with geometric objects defined on certain manifolds such that one obtains a coordinate free description of the systems.
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Series Editors: The Rectors Manuel Garcia Velarde - Madrid Jean Salen9on - Palaiseau Wilhelm Schneider - Wien
The Secretary General Bernhard Schrefter - Padua
Executive Editor Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES- No. 444
ADVANCED DYNAMICS AND CONTROL OF STRUCTURES AND MACHINES
EDITED BY HANS IRSCHIK JOHANNES KEPLER UNIVERSITY OF LINZ KURTSCHLACHER JOHANNES KEPLER UNIVERSITY OF LINZ
Springer-Verlag Wien GmbH
This volume contains 63 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting,' re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2004 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 2004
SPIN 11313434
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-22867-8 ISBN 978-3-7091-2774-2 (eBook) DOI 10.1007/978-3-7091-2774-2
PREFACE
Advanced dynamics and control of structures and machines represents an upto-date, multi-disciplinary field in engineering. It brings together researchers in mechanical, civil and control engineering, and in applied mathematics. This book is a result of the Advanced School entitled "Advanced Dynamics of Structures and Machines", which took place in the International Centre for Mechanical Sciences (CISM}, Udine, Italy, during April15-Jg, 2002. It was the aim of this school to present modern foundations and methods of modeling and control of flexible structures and machines, under operating as well as under severe loading conditions. The need to understand such advanced formulations for deformable mechanical systems is evident, especially in problems of automotive engineering, of robotics, in rotating machinery and for civil engineering structures. The collection of lecture notes given in this book is an attempt to introduce the basic ideas of dynamics and control, to provide scientific knowledge for these fast expanding fields, as well as to present up-to-date research. The book starts with a concise introduction into the models and equations of continuum mechanics, including the laws of thermodynamics and a discussion on the form of the constitutive relations for materials. Afterwards, the balance equations and jump relations of continuum mechanics are reviewed with a special emphasis upon the validity and consiste
