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Geometry of nonholonomically constrained systems

Autore: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
Editore: Singapore ; Hackensack, NJ : World Scientific, ©2010.
Serie: Advanced series in nonlinear dynamics, v. 26.
Edizione/Formato:   Libro : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
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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  Per saperne di più…
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Tipo documento: Book
Tutti gli autori / Collaboratori: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
ISBN: 9789814289481 9814289485
Numero OCLC: 410223593
Descrizione: xvi, 404 pages : illustrations ; 24 cm.
Contenuti: 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.
Titolo della serie: Advanced series in nonlinear dynamics, v. 26.
Responsabilità: Richard Cushman, Hans Duistermaat, Jędrzej Śniatycki.

Abstract:

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  Per saperne di più…

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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 Per saperne di più…

 
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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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