| Author | : Francesco Bullo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 756 |
| Release | : 2004-11-04 |
| Genre | : Science |
| ISBN | : 9780387221953 |
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
| Author | : Francesco Bullo |
| Publisher | : Springer |
| Total Pages | : 727 |
| Release | : 2019-06-12 |
| Genre | : Science |
| ISBN | : 1489972765 |
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
| Author | : A.M. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 498 |
| Release | : 2008-02-03 |
| Genre | : Mathematics |
| ISBN | : 0387216448 |
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.
| Author | : Andrei A. Agrachev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 440 |
| Release | : 2004-04-15 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9783540210191 |
This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.
| Author | : Velimir Jurdjevic |
| Publisher | : Cambridge University Press |
| Total Pages | : 516 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0521495024 |
Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
| Author | : A.M. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 501 |
| Release | : 2007-09-27 |
| Genre | : Mathematics |
| ISBN | : 0387955356 |
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.
| Author | : Jerrold E. Marsden |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1992-04-30 |
| Genre | : Mathematics |
| ISBN | : 9780521428446 |
Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.
| Author | : Jerrold E. Marsden |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 593 |
| Release | : 2013-03-19 |
| Genre | : Science |
| ISBN | : 0387217924 |
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
| Author | : Jorge Cortés Monforte |
| Publisher | : Springer |
| Total Pages | : 235 |
| Release | : 2004-10-19 |
| Genre | : Mathematics |
| ISBN | : 3540457305 |
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.
