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

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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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Editorial Reviews

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Nine papers from the June 1996 conference focus on research directions having origins in mechanics and differential geometry, but driven by modern control theory. Among the topics: lie determined systems and optimal problems with symmetries; Dubins' problem in the hyperbolic plane using the open disc model; and geometry and structure in the control of linear time invariant systems. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Lie determined systems and optimal problems with symmetries 1
Sub-Riemannian metrics on R[superscript 3] 29
Sub-Riemannian Geometry: the Martinet Case 79
Dubins' problem in hyperbolic space 101
Dubins' problem in the hyperbolic plane using the open disc model 115
Three dimensional non-Euclidean Dubins' problem 153
Symmetries of nonlinear control systems and their symbols 183
The motion of a sphere on a surface of revolution: a geometric approach 199
Geometry and Structure in the Control of Linear Time Invariant Systems 221
Index 237
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