Geometric control and non-holonomic mechanics : Conference on Geometric Control and Non-Holonomic Mechanics, June 19-21, 1996, Mexico City
著者
書誌事項
Geometric control and non-holonomic mechanics : Conference on Geometric Control and Non-Holonomic Mechanics, June 19-21, 1996, Mexico City
（Conference proceedings / Canadian Mathematical Society, v. 25）
American Mathematical Society for the Canadian Mathematical Society, c1998
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 geometry 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.
目次
Lie 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.
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