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Reduction Symmetry And Phases In Mechanics
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Book Synopsis Reduction, Symmetry, and Phases in Mechanics by : Jerrold E. Marsden
Download or read book Reduction, Symmetry, and Phases in Mechanics written by Jerrold E. Marsden and published by American Mathematical Soc.. This book was released on 1990 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various holonomy phenomena are shown to be instances of the reconstruction procedure for mechanical systems with symmetry. We systematically exploit this point of view for fixed systems and for slowly moving systems in adiabatic context. For the latter, we obtain the phases as the holonomy for a connection which synthesizes the Cartan connection for moving mechanical systems with the Hannay-Berry connection for integrable systems.
Author :Stephanie Frank Singer Publisher :Springer Science & Business Media ISBN 13 :1461201896 Total Pages :201 pages Book Rating :4.4/5 (612 download)
Book Synopsis Symmetry in Mechanics by : Stephanie Frank Singer
Download or read book Symmetry in Mechanics written by Stephanie Frank Singer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: "And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.
Book Synopsis Hamiltonian Reduction by Stages by : Jerrold E. Marsden
Download or read book Hamiltonian Reduction by Stages written by Jerrold E. Marsden and published by Springer. This book was released on 2007-06-05 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Book Synopsis Lectures on Mechanics by : Jerrold E. Marsden
Download or read book Lectures on Mechanics written by Jerrold E. Marsden and published by Cambridge University Press. This book was released on 1992-04-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Phases In Physics by : Alfred Shapere
Download or read book Geometric Phases In Physics written by Alfred Shapere and published by World Scientific. This book was released on 1989-07-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.
Book Synopsis Introduction to Mechanics and Symmetry by : Jerrold E. Marsden
Download or read book Introduction to Mechanics and Symmetry written by Jerrold E. Marsden and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Motion, Control, and Geometry by : National Research Council
Download or read book Motion, Control, and Geometry written by National Research Council and published by National Academies Press. This book was released on 1997-05-07 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lagrangian Reduction by Stages by : Hernán Cendra
Download or read book Lagrangian Reduction by Stages written by Hernán Cendra and published by American Mathematical Soc.. This book was released on 2001 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler-Poincare reduction (for the case in which the configuration space is a Lie group) as well as Euler-Poincare reduction for semidirect products.
Book Synopsis Algorithmic Foundation of Robotics VII by : Srinivas Akella
Download or read book Algorithmic Foundation of Robotics VII written by Srinivas Akella and published by Springer Science & Business Media. This book was released on 2008-07-10 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms are a fundamental component of robotic systems: they control or reason about motion and perception in the physical world. They receive input from noisy sensors, consider geometric and physical constraints, and operate on the world through imprecise actuators. The design and analysis of robot algorithms therefore raises a unique combination of questions in control theory, computational and differential geometry, and computer science. This book contains the proceedings from the 2006 Workshop on the Algorithmic Foundations of Robotics. This biannual workshop is a highly selective meeting of leading researchers in the field of algorithmic issues related to robotics. The 32 papers in this book span a wide variety of topics: from fundamental motion planning algorithms to applications in medicine and biology, but they have in common a foundation in the algorithmic problems of robotic systems.
Author :Yurii Aleksandrovich Izyumov Publisher :Springer Science & Business Media ISBN 13 :9400919204 Total Pages :462 pages Book Rating :4.4/5 (9 download)
Book Synopsis Phase Transitions and Crystal Symmetry by : Yurii Aleksandrovich Izyumov
Download or read book Phase Transitions and Crystal Symmetry written by Yurii Aleksandrovich Izyumov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: About half a century ago Landau formulated the central principles of the phe nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.
Author : Publisher :World Scientific ISBN 13 :1911299360 Total Pages :375 pages Book Rating :4.9/5 (112 download)
Download or read book written by and published by World Scientific. This book was released on with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Mechanics and Symmetry by : James Montaldi
Download or read book Geometric Mechanics and Symmetry written by James Montaldi and published by Cambridge University Press. This book was released on 2005-05-05 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.
Book Synopsis Developments and Trends in Infinite-Dimensional Lie Theory by : Karl-Hermann Neeb
Download or read book Developments and Trends in Infinite-Dimensional Lie Theory written by Karl-Hermann Neeb and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Book Synopsis Momentum Maps and Hamiltonian Reduction by : Juan-Pablo Ortega
Download or read book Momentum Maps and Hamiltonian Reduction written by Juan-Pablo Ortega and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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.
Book Synopsis Nonconservative Stability Problems of Modern Physics by : Oleg N. Kirillov
Download or read book Nonconservative Stability Problems of Modern Physics written by Oleg N. Kirillov and published by Walter de Gruyter. This book was released on 2013-06-26 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work gives a complete overview on the subject of nonconservative stability from the modern point of view. Relevant mathematical concepts are presented, as well as rigorous stability results and numerous classical and contemporary examples from mechanics and physics. It deals with both finite- and infinite-dimensional nonconservative systems and covers the fundamentals of the theory, including such topics as Lyapunov stability and linear stability analysis, Hamiltonian and gyroscopic systems, reversible and circulatory systems, influence of structure of forces on stability, and dissipation-induced instabilities, as well as concrete physical problems, including perturbative techniques for nonself-adjoint boundary eigenvalue problems, theory of the destabilization paradox due to small damping in continuous circulatory systems, Krein-space related perturbation theory for the MHD kinematic mean field α2-dynamo, analysis of Campbell diagrams and friction-induced flutter in gyroscopic continua, non-Hermitian perturbation of Hermitian matrices with applications to optics, and magnetorotational instability and the Velikhov-Chandrasekhar paradox. The book serves present and prospective specialists providing the current state of knowledge in the actively developing field of nonconservative stability theory. Its understanding is vital for many areas of technology, ranging from such traditional ones as rotor dynamics, aeroelasticity and structural mechanics to modern problems of hydro- and magnetohydrodynamics and celestial mechanics.
Book Synopsis Classical and Quantum Dynamics by : Walter Dittrich
Download or read book Classical and Quantum Dynamics written by Walter Dittrich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here a detailed treatment many worked examples. This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.
Book Synopsis Dynamics and Control of Mechanical Systems: The Falling Cat and Related Problems by : Michael J. Enos
Download or read book Dynamics and Control of Mechanical Systems: The Falling Cat and Related Problems written by Michael J. Enos and published by American Mathematical Soc.. This book was released on 1993 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of papers presented at the Fields Institute workshop, ``The Falling Cat and Related Problems,'' held in March 1992. The theme of the workshop was the application of methods from geometric mechanics and mathematical control theory to problems in the dynamics and control of freely rotating systems of coupled rigid bodies and related nonholonomic mechanical systems. This book will prove useful in providing insight into this new and exciting area of research.
