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Geometry of nonholonomically constrained systems

作者: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
出版商: Singapore ; Hackensack, NJ : World Scientific, ©2010.
叢書: Advanced series in nonlinear dynamics, v. 26.
版本/格式:   圖書 : 英語所有版本和格式的總覽
資料庫: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  再讀一些...
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文件類型: 圖書
所有的作者/貢獻者: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
ISBN: 9789814289481 9814289485
OCLC系統控制編碼: 410223593
描述: xvi, 404 p. : ill. ; 24 cm.
内容: 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.
叢書名: Advanced series in nonlinear dynamics, v. 26.
責任: Richard Cushman, Hans Duistermaat, Jędrzej Śniatycki.

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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  再讀一些...

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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 再讀一些...

 
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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."--BOOK JACKET."
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