Geometric Control and Non-Holonomic Mechanics: Conference on Geometric Control and Non-Holomorphic Mechanics, June 19-21, 1996, Mexico City

Geometric Control and Non-Holonomic Mechanics: Conference on Geometric Control and Non-Holomorphic Mechanics, June 19-21, 1996, Mexico City

by Velimir Jurdjevic
     
 

ISBN-10: 0821807951

ISBN-13: 9780821807958

Pub. Date: 09/11/1998

Publisher: American Mathematical Society

Control 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

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Overview

Control 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 analyzed 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.

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Product Details

ISBN-13:
9780821807958
Publisher:
American Mathematical Society
Publication date:
09/11/1998
Series:
Conference Proceedings of the Canadian Mathematical Society Series, #25
Pages:
239
Product dimensions:
7.09(w) x 10.24(h) x (d)

Table of Contents

Preface
Lie determined systems and optimal problems with symmetries1
Sub-Riemannian metrics on R[superscript 3]29
Sub-Riemannian Geometry: the Martinet Case79
Dubins' problem in hyperbolic space101
Dubins' problem in the hyperbolic plane using the open disc model115
Three dimensional non-Euclidean Dubins' problem153
Symmetries of nonlinear control systems and their symbols183
The motion of a sphere on a surface of revolution: a geometric approach199
Geometry and Structure in the Control of Linear Time Invariant Systems221
Index237

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