Geometric Control And Non Holonomic Mechanics
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Geometric Control and Non-holonomic Mechanics
Author: Velimir Jurdjevic
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
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 copyrighted by Book News, Inc., Portland, OR
Nonholonomic Mechanics and Control
Author: A.M. Bloch
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-02-03
Our goal in this book is to explore some of the connections between control theory and geometric mechanics; that is, we link control theory with a g- metric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems s- ject to motion constraints. This synthesis of topics is appropriate, since there is a particularly rich connection between mechanics and nonlinear control theory. While an introduction to many important aspects of the mechanics of nonholonomically constrained systems may be found in such sources as the monograph of Neimark and Fufaev [1972], the geometric view as well as the control theory of such systems remains largely sc- tered through various research journals. Our aim is to provide a uni?ed treatment of nonlinear control theory and constrained mechanical systems that will incorporate material that has not yet made its way into texts and monographs. Mechanicshastraditionallydescribedthebehavioroffreeandinteracting particles and bodies, the interaction being described by potential forces. It encompasses the Lagrangian and Hamiltonian pictures and in its modern form relies heavily on the tools of di?erential geometry (see, for example, Abraham and Marsden [1978]and Arnold [1989]). From our own point of view,ourpapersBloch,Krishnaprasad,Marsden,andMurray[1996],Bloch and Crouch [1995], and Baillieul [1998] have been particularly in?uential in the formulations presented in this book. Control Theory and Nonholonomic Systems. Control theory is the theory of prescribing motion for dynamical systems rather than describing vi Preface their observed behavior.
Geometric, Control and Numerical Aspects of Nonholonomic Systems
Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.