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Geometry of nonholonomically constrained systems

Autor Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
Vydavatel: Singapore ; Hackensack, NJ : World Scientific, ©2010.
Edice: Advanced series in nonlinear dynamics, v. 26.
Vydání/formát:   Kniha : EnglishZobrazit všechny vydání a formáty
Databáze:WorldCat
Shrnutí:
"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  Přečíst více...
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Detaily

Typ dokumentu: Book
Všichni autoři/tvůrci: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
ISBN: 9789814289481 9814289485
OCLC číslo: 410223593
Popis: xvi, 404 pages : illustrations ; 24 cm.
Obsahy: Nonholonomically Constrained Motions; Group Actions and Orbit Spaces; Symmetry and Reduction; Reconstruction, Relative Equilibria and Periodic Orbits; Caratheodory's Sleigh; Convex Rolling Rigid Body; The Rolling Disk.
Název edice: Advanced series in nonlinear dynamics, v. 26.
Odpovědnost: Richard Cushman, Hans Duistermaat, Jędrzej Śniatycki.

Anotace:

Offers a modern differential geometric treatment of linearly nonholonomically constrained systems. This title discusses what is meant by symmetry of such a system and gives a general theory of how to  Přečíst více...

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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 Přečíst více...

 
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schema:reviewBody""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."--Jacket."
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