Free Delivery Over $100
|
|
|||
|
||||
OverviewControl theory, a synthesis of geometric theory of differential equations enriched with variational principles and the associated symplectic geometry, emerges as a new mathematical subject of interest to engineers, mathematicians, and physicists. This collection of articles focuses on several distinctive research directions having origins in mechanics and differential geometry, but driven by modern control theory. The first of these directions deals with the singularities of small balls for problems of sub-Riemannian geomtery and provides a generic classification of singularities for two-dimensional distributions of contact type in a three-dimensional ambient space. The second direction deals with invariant optimal problems on Lie groups exemplified through the problem of Dublins extended to symmetric spaces, the elastic problem of Kirchhoff and its relation to the heavy top. The results described in the book are explicit and demonstrate convincingly the power of geometric formalism. The remaining directions deal with the geometric nature of feedback analysed through the language of fiber bundles, and the connections of geometric control to non-holonomic problems in mechanics, as exemplified through the motions of a sphere on surfaces of revolution. This book provides quick access to new research directions in geometric control theory. It also demonstrates the effectiveness of new insights and methods that control theory brings to mechanics and geometry. Full Product DetailsAuthor: Velimir Jurdjevic , R.W. SharpePublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 25 Weight: 0.454kg ISBN: 9780821807958ISBN 10: 0821807951 Pages: 239 Publication Date: 30 September 1998 Recommended Age: From To 19 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsLie determined systems and optimal problems with symmetries by V. Jurdjevic Sub-Riemannian metrics on ${\mathbb{R}^3}$ by A. A. Agrachev, El C. El-A., and J. P. Gauthier Sub-Riemannian geometry: the Martinet case by B. Bonnard and M. Chyba Dubins' problem in hyperbolic space by D. Mittenhuber Dubins' problem in the hyperbolic plane using the open disc model by D. Mittenhuber Three dimensional non-Euclidean Dubins' problem by F. Monroy-Perez Symmetries of nonlinear control systems and their symbols by B. Jakubczyk The motion of a sphere on a surface of revolution: a geometric approach by J. L. F. Chapou Geometry and structure in the control of linear time invariant systems by J. C. Martinez-Garcia Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
