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Geometry of nonholonomically constrained systems

Autor: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
Editorial: Singapore ; Hackensack, NJ : World Scientific, ©2010.
Serie: Advanced series in nonlinear dynamics, v. 26.
Edición/Formato:   Libro : Inglés (eng)Ver todas las ediciones y todos los formatos
Base de datos:WorldCat
Resumen:
"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  Leer más
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Detalles

Tipo de documento: Libro/Texto
Todos autores / colaboradores: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
ISBN: 9789814289481 9814289485
Número OCLC: 410223593
Descripción: xvi, 404 pages : illustrations ; 24 cm.
Contenido: 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.
Título de la serie: Advanced series in nonlinear dynamics, v. 26.
Responsabilidad: Richard Cushman, Hans Duistermaat, Jędrzej Śniatycki.

Resumen:

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  Leer más

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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 Leer más

 
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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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