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Geometry of nonholonomically constrained systems

Author: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
Publisher: New Jersey : World Scientific, ©2010.
Series: Advanced series in nonlinear dynamics, v. 26.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cushman, Richard H., 1942-
Geometry of nonholonomically constrained systems.
Singapore ; Hackensack, NJ : World Scientific, ©2010
(DLC) 2009024384
(OCoLC)410223593
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Richard H Cushman; J J Duistermaat; Jędrzej Śniatycki
ISBN: 9789814289498 9814289493
OCLC Number: 630164386
Description: 1 online resource (xvi, 404 pages) : illustrations (some color).
Contents: Nonholonomically constrained motions. Newton's equations --
Constraints --
Lagrange-d'Alembert equations --
Lagrange derivative --
Hamilton-d'Alembert equations --
Distributional Hamiltonian formulation --
Almost Poisson brackets --
Momenta and momentum equation --
Projection principle --
Accessible sets --
Constants of motion --
Notes --
Group actions and orbit spaces. Group actions --
Orbit spaces --
Isotropy and orbit types --
Smooth structure on an orbit space --
Subcartesian spaces --
Stratification of the orbit space by orbit types --
Derivations and vector fields on a differential space --
Vector fields on a stratified differential space --
Vector fields on an orbit space --
Tangent objects to an orbit space --
Notes --
Symmetry and reduction. Dynamical systems with symmetry --
Nonholonomic singular reduction --
Nonholonomic regular reduction --
Chaplygin systems --
Orbit types and reduction --
Conservation laws --
Lifted actions and the momentum equation --
Notes --
Reconstruction, relative equilibria and relative periodic orbits. Reconstruction --
Relative equilibria --
Relative periodic orbits --
Notes --
Carathéodory's sleigh. Basic set up --
Equations of motion --
Reduction of the E(2) symmetry --
Motion on the E(2) reduced phase space --
Reconstruction --
Notes --
Convex rolling rigid body. Basic set up --
Unconstrained motion --
Constraint distribution --
Constrained equations of motion --
Reduction of the translational [symbol] symmetry --
Reduction of E(2) symmetry --
Body of revolution --
Notes --
The rolling disk. General set up --
Reduction of the E(2) x S[symbol] symmetry --
Reconstruction --
Relative equilibria --
A potential function on an interval --
Scaling --
Solutions of the rescaled Chaplygin equations --
Bifurcations of a vertical disk --
The global geometry of the degeneracy locus --
Falling flat. --
Near falling flat --
The bifurcation diagram --
The integral map --
Constant energy slices --
The spatial rotational shift --
Notes.
Series Title: Advanced series in nonlinear dynamics, v. 26.
Responsibility: 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  Read more...

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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 Read more...

 
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