TY  - GEN
T1  - Geometry of nonholonomically constrained systems
T2  - Advanced series in nonlinear dynamics ;
A1  - Cushman, Richard H., 1942-
A2  - Duistermaat, J. J. (Johannes Jisse), 1942-2010
A2  - Śniatycki, Jędrzej
LA  - English
PP  - New Jersey
PB  - World Scientific
YR  - 2010
UL  - https://ebooks.jgu.edu.in/Record/ebsco_acadsubs_ocn630164386
AB  - 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.
OP  - 404
CN  - QA614.833 .C87 2010eb
SN  - 9789814289498
SN  - 9814289493
SN  - 9789814289481
SN  - 9814289485
KW  - Geometry, Differential.
KW  - Nonholonomic dynamical systems.
KW  - Rigidity (Geometry)
KW  - Caratheodory measure.
KW  - Géométrie différentielle.
KW  - Systèmes non holonomes.
KW  - Rigidité (Géométrie)
KW  - Mesure de Carathéodory.
KW  - MATHEMATICS : Geometry : Differential.
KW  - Caratheodory measure
KW  - Geometry, Differential
KW  - Nonholonomic dynamical systems
KW  - Geometry.
KW  - Mathematics.
KW  - Physical Sciences & Mathematics.
KW  - Differentialgeometrie : Mechanik.
KW  - Mechanik : Differentialgeometrie.
ER  -