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
大学図書館所蔵 全27件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
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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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