Reduction Symmetry And Phases In Mechanics
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Reduction Symmetry And Phases In Mechanics
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Author : Jerrold E. Marsden
language : en
Publisher:
Release Date : 1990
Reduction Symmetry And Phases In Mechanics written by Jerrold E. Marsden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Holonomy groups categories.
Reduction Symmetry And Phases In Mechanics
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Author : Jerrold E. Marsden
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Reduction Symmetry And Phases In Mechanics written by Jerrold E. Marsden 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 1990 with Mathematics categories.
Motion Control And Geometry
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1997-05-07
Motion Control And Geometry written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-07 with Mathematics categories.
Some of the modem developments described in Motion, Control, and Geometry include the geometric control of robot motion and craft orientation, how high-power precision micromotors are engineered for less invasive surgery and self-focusing lens applications, what a mobile robot on a surface has in common with one moving in three dimensions, and how the motion-control problem is simplified by a coupled oscillator's geometric grouping of degrees of freedom and motion time scales. The four papers in these proceedings provide a view through the scientific portal of today's motion-control geometric research into tomorrow's technology. The mathematics needed to carry out this research is that of modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student's education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of "motion"-that of students entering Plato's Academy, where the following caveat was inscribed above the doorway: "Let no one ignorant of geometry enter here." Readers of these chapters will gain an appreciation of modem geometry and how it continues to play a crucial role in the context of motion control in cutting-edge science and technology.
Geometric Mechanics Dynamics And Symmetry
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Author : Darryl D. Holm
language : en
Publisher: Imperial College Press
Release Date : 2008-01-01
Geometric Mechanics Dynamics And Symmetry 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 2008-01-01 with Mathematics categories.
Advanced undergraduate and graduate students in mathematics, physics and engineering.
Momentum Maps And Hamiltonian Reduction
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Author : Juan-Pablo Ortega
language : en
Publisher: Birkhäuser
Release Date : 2013-02-14
Momentum Maps And Hamiltonian Reduction written by Juan-Pablo Ortega and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with Mathematics categories.
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Introduction To Mechanics And Symmetry
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Author : Jerrold E. Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Introduction To Mechanics And Symmetry written by Jerrold E. Marsden 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 2013-03-19 with Science categories.
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.
Geometric Phases In Classical And Quantum Mechanics
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Author : Dariusz Chruscinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Phases In Classical And Quantum Mechanics written by Dariusz Chruscinski 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 Mathematics categories.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Momentum Maps And Hamiltonian Reduction
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Author : Juan-Pablo Ortega
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Momentum Maps And Hamiltonian Reduction written by Juan-Pablo Ortega 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 2013-04-17 with Mathematics categories.
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Geometry Mechanics And Control In Action For The Falling Cat
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Author : Toshihiro Iwai
language : en
Publisher: Springer Nature
Release Date : 2021-04-23
Geometry Mechanics And Control In Action For The Falling Cat written by Toshihiro Iwai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.
The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat. In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.
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.