Geometry Of Nonholonomically Constrained Systems
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A01=Hans Duistermaat
A01=Jedrzej Sniatycki
A01=Richard H Cushman
Author_Hans Duistermaat
Author_Jedrzej Sniatycki
Author_Richard H Cushman
CarathAfA(C)odory's Sleigh
Caratheodory's Sleigh
Carathéodory's Sleigh
Category=PBMP
Convex Rigid Body
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Nonholonomic Constrained System
Rolling Disk
Symmetry Reduction
Product details
- ISBN 9789814289481
- Publication Date: 11 Dec 2009
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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 Carathéodory'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.
