GEOMETRY OF NONHOLONOMICALLY CONS..(V26) (Advanced Series in Nonlinear Dynamics, 26, Band 26) - Hardcover

Al Richard Cushman Et

 
9789814289481: GEOMETRY OF NONHOLONOMICALLY CONS..(V26) (Advanced Series in Nonlinear Dynamics, 26, Band 26)
Hardcover
ISBN 10: 9814289485 ISBN 13: 9789814289481
Verlag: World Scientific, 2009

Inhaltsangabe

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.

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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.

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Verlag
World Scientific
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
9814289485
ISBN 13 
9789814289481
Einband
Gebundene Ausgabe
Anzahl der Seiten
422
Kontakt zum Hersteller
preigu GmbH & Co. KG
mail@preigu.de

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Osnabrück
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