Overview

This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Caratheodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat.The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trail-blazers in their respective fields.

Full Product Details

Author:   Richard H Cushman (Univ Of Calgary, Canada) ,  Hans Duistermaat (Univ Utrecht, The Netherlands) ,  Jedrzej Sniatycki (Univ Of Calgary, Canada)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   26
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 22.90cm
Weight:   0.771kg
ISBN:  

9789814289481

ISBN 10:   9814289485
Pages:   424
Publication Date:   11 December 2009
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Reviews

I consider this book as a fundamental reference on nonholonomic dynamics. It covers a broad variety of topics and problems covering these kinds of systems. It shows the importance of the geometric study of dynamical systems for integrability and qualitative analysis. -- Mathematical Reviews Mathematical Reviews

"I consider this book as a fundamental reference on nonholonomic dynamics. It covers a broad variety of topics and problems covering these kinds of systems. It shows the importance of the geometric study of dynamical systems for integrability and qualitative analysis. -- Mathematical Reviews ""Mathematical Reviews"""

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