عنوان

Geometry of nonholonomically constrained systems /

شابک

9789814289498

شابک

9814289493

شابک اشتباه

9789814289481

شابک اشتباه

9814289485

شماره

b779273

عنوان اصلي

Geometry of nonholonomically constrained systems /

نام عام مواد

[Book]

نام نخستين پديدآور

Richard Cushman, Hans Duistermaat, Jędrzej Śniatycki.

محل نشرو پخش و غیره

New Jersey :

نام ناشر، پخش کننده و غيره

World Scientific,

تاریخ نشرو بخش و غیره

©2010.

نام خاص و کميت اثر

1 online resource (xvi, 404 pages) :

ساير جزييات

illustrations (some color).

عنوان فروست

Advanced series in nonlinear dynamics ;

مشخصه جلد

v. 26

متن يادداشت

Includes bibliographical references (pages 387-393) and index.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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 Carathéodory'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.

عنوان

Geometry of nonholonomically constrained systems.

شماره استاندارد بين المللي کتاب و موسيقي

9789814289481

موضوع مستند نشده

Caratheodory measure.

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

Nonholonomic dynamical systems.

موضوع مستند نشده

Rigidity (Geometry)

موضوع مستند نشده

Caratheodory measure.

موضوع مستند نشده

Differentialgeometrie-- Mechanik.

موضوع مستند نشده

Geometry, Differential.

موضوع مستند نشده

Geometry.

موضوع مستند نشده

MATHEMATICS-- Geometry-- Differential.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Mechanik-- Differentialgeometrie.

موضوع مستند نشده

Nonholonomic dynamical systems.

موضوع مستند نشده

Physical Sciences & Mathematics.

موضوع مستند نشده

Rigidity (Geometry)

موضوع مستند نشده

MAT-- 012030

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Cushman, Richard H.,1942-

مستند نام اشخاص تاييد نشده

Duistermaat, J. J., (Johannes Jisse),1942-

مستند نام اشخاص تاييد نشده

Śniatycki, Jędrzej.

تاريخ عمليات

20201206182513.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y