Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition
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Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition
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Author : Darryl D Holm
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-07-13
Geometric Mechanics Part I Dynamics And Symmetry 2nd Edition written by Darryl D Holm and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-13 with Mathematics categories.
See also GEOMETRIC MECHANICS — Part II: Rotating, Translating and Rolling (2nd Edition) This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton's principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. In particular, the role of Noether's theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications./a
Geometric Mechanics And Symmetry
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Author : Darryl D. Holm
language : en
Publisher: Oxford University Press
Release Date : 2009-07-30
Geometric Mechanics And Symmetry written by Darryl D. Holm and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincaré equations for dynamics on Lie groups. Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincaré reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.
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.
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.
Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text 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 on-line.
Mathematical Methods Of Classical Mechanics
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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Mathematical Methods Of Classical Mechanics written by V.I. Arnol'd 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 2013-04-09 with Mathematics categories.
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Geometric Control Theory
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Author : Velimir Jurdjevic
language : en
Publisher: Cambridge University Press
Release Date : 1997
Geometric Control Theory written by Velimir Jurdjevic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
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 Mechanics Part Ii Rotating Translating And Rolling 2nd Edition
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Author : Darryl D Holm
language : en
Publisher: World Scientific
Release Date : 2011-10-31
Geometric Mechanics Part Ii Rotating Translating And Rolling 2nd Edition written by Darryl D Holm and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-31 with Mathematics categories.
See also GEOMETRIC MECHANICS — Part I: Dynamics and Symmetry (2nd Edition) This textbook introduces modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. In particular, it explains the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint by formulating their solutions as coadjoint motions generated by Lie groups. The only prerequisites are linear algebra, multivariable calculus and some familiarity with Euler-Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The book uses familiar concrete examples to explain variational calculus on tangent spaces of Lie groups. Through these examples, the student develops skills in performing computational manipulations, starting from vectors and matrices, working through the theory of quaternions to understand rotations, then transferring these skills to the computation of more abstract adjoint and coadjoint motions, Lie-Poisson Hamiltonian formulations, momentum maps and finally dynamics with nonholonomic constraints.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. Many worked examples of adjoint and coadjoint actions of Lie groups on smooth manifolds have also been added and the enhanced coursework examples have been expanded. The second edition is ideal for classroom use, student projects and self-study./a
Dynamical Symmetry
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Author : Carl Wulfman
language : en
Publisher: World Scientific
Release Date : 2011
Dynamical Symmetry written by Carl Wulfman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.