Geometric Control And Non Holonomic Mechanics
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Geometric Control And Non Holonomic Mechanics
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Author : Velimir Jurdjevic
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Geometric Control And Non Holonomic Mechanics written by Velimir Jurdjevic and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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 analysed 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.
Nonholonomic Mechanics And Control
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Author : A.M. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-27
Nonholonomic Mechanics And Control written by A.M. Bloch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-27 with Mathematics categories.
This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
Nonholonomic Mechanics And Control
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Author : A.M. Bloch
language : en
Publisher: Springer
Release Date : 2015-11-05
Nonholonomic Mechanics And Control written by A.M. Bloch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-05 with Science categories.
This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
Geometric Control And Numerical Aspects Of Nonholonomic Systems
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Author : Jorge Cortés Monforte
language : en
Publisher: Springer
Release Date : 2004-10-19
Geometric Control And Numerical Aspects Of Nonholonomic Systems written by Jorge Cortés Monforte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
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.
Mechanics Of Non Holonomic Systems
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Author : Sh.Kh Soltakhanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-27
Mechanics Of Non Holonomic Systems written by Sh.Kh Soltakhanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-27 with Technology & Engineering categories.
A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. The system of equations of motion in the generalized coordinates is regarded as a one vector relation, represented in a space tangential to a manifold of all possible positions of system at given instant. The tangential space is partitioned by the equations of constraints into two orthogonal subspaces. In one of them for the constraints up to the second order, the motion low is given by the equations of constraints and in the other one for ideal constraints, it is described by the vector equation without reactions of connections. In the whole space the motion low involves Lagrangian multipliers. It is shown that for the holonomic and nonholonomic constraints up to the second order, these multipliers can be found as the function of time, positions of system, and its velocities. The application of Lagrangian multipliers for holonomic systems permits us to construct a new method for determining the eigenfrequencies and eigenforms of oscillations of elastic systems and also to suggest a special form of equations for describing the system of motion of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as programming constraints such that their validity is provided due to the existence of generalized control forces, which are determined as the functions of time. The closed system of differential equations, which makes it possible to find as these control forces, as the generalized Lagrange coordinates, is compound. The theory suggested is illustrated by the examples of a spacecraft motion. The book is primarily addressed to specialists in analytic mechanics.
Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning
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Author : Frédéric Jean
language : en
Publisher: Springer
Release Date : 2014-07-17
Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning written by Frédéric Jean and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-17 with Science categories.
Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.
Analysis And Geometry In Control Theory And Its Applications
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Author : Piernicola Bettiol
language : en
Publisher: Springer
Release Date : 2015-09-01
Analysis And Geometry In Control Theory And Its Applications written by Piernicola Bettiol and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-01 with Mathematics categories.
Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.
Geometric Mechanics Rotating Translating And Rolling
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Author : Darryl D. Holm
language : en
Publisher: Imperial College Press
Release Date : 2008
Geometric Mechanics Rotating Translating And Rolling written by Darryl D. Holm and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
Introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. This book treats the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint, by formulating their solutions as coadjoint motions generated by Lie groups.
Dynamics Of Nonholonomic Systems
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Author : Ju. I. Neimark
language : en
Publisher: American Mathematical Soc.
Release Date : 1972
Dynamics Of Nonholonomic Systems written by Ju. I. Neimark and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Nonholonomic Motion Planning
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Author : Zexiang Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonholonomic Motion Planning written by Zexiang Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Nonholonomic Motion Planning grew out of the workshop that took place at the 1991 IEEE International Conference on Robotics and Automation. It consists of contributed chapters representing new developments in this area. Contributors to the book include robotics engineers, nonlinear control experts, differential geometers and applied mathematicians. Nonholonomic Motion Planning is arranged into three chapter groups: Controllability: one of the key mathematical tools needed to study nonholonomic motion. Motion Planning for Mobile Robots: in this section the papers are focused on problems with nonholonomic velocity constraints as well as constraints on the generalized coordinates. Falling Cats, Space Robots and Gauge Theory: there are numerous connections to be made between symplectic geometry techniques for the study of holonomies in mechanics, gauge theory and control. In this section these connections are discussed using the backdrop of examples drawn from space robots and falling cats reorienting themselves. Nonholonomic Motion Planning can be used either as a reference for researchers working in the areas of robotics, nonlinear control and differential geometry, or as a textbook for a graduate level robotics or nonlinear control course.