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Geometric Mechanics Dynamics And Symmetry
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Book Synopsis Geometric Mechanics: Dynamics and symmetry by : Darryl D. Holm
Download or read book Geometric Mechanics: Dynamics and symmetry written by Darryl D. Holm and published by Imperial College Press. This book was released on 2008-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and graduate students in mathematics, physics and engineering.
Book Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm
Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.
Book Synopsis Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) by : Holm Darryl D
Download or read book Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) written by Holm Darryl D and published by World Scientific Publishing Company. This book was released on 2011-07-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Geometric Mechanics by : Darryl D Holm
Download or read book Geometric Mechanics written by Darryl D Holm and published by World Scientific Publishing Company. This book was released on 2008-04-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. It 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. 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. Variational calculus on tangent spaces of Lie groups is explained in the context of familiar concrete examples. 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, and 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 120 Exercises and 55 Worked Answers help the student to grasp the essential aspects of the subject, and to develop proficiency in using the powerful methods of geometric mechanics. In addition, all theorems are stated and proved explicitly. The book's many examples and worked exercises make it ideal for both classroom use and self-study. Contents: GalileoNewton, Lagrange, HamiltonQuaternionsQuaternionic ConjugacySpecial Orthogonal GroupThe Special Euclidean GroupGeometric Mechanics on SE(3)Heavy Top EquationsThe Euler–Poincaré TheoremLie–Poisson Hamiltonian FormMomentum MapsRound Rolling Rigid Bodies Readership: Advanced undergraduate and graduate students in mathematics, physics and engineering; researchers interested in learning the basic ideas in the fields; non-experts interested in geometric mechanics, dynamics and symmetry.
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 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 Dynamical Symmetry by : Carl Wulfman
Download or read book Dynamical Symmetry written by Carl Wulfman and published by World Scientific. This book was released on 2011 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry by : Kai S Lam
Download or read book Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry written by Kai S Lam and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern-Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.
Book Synopsis Geometric Mechanics: Rotating, translating and rolling by : Darryl D. Holm
Download or read book Geometric Mechanics: Rotating, translating and rolling written by Darryl D. Holm and published by Imperial College Press. This book was released on 2008 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Mechanics and Symmetry by : James Montaldi
Download or read book Geometric Mechanics and Symmetry written by James Montaldi and published by . This book was released on 2005 with total page 414 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 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 Mechanics by : Waldyr Muniz Oliva
Download or read book Geometric Mechanics written by Waldyr Muniz Oliva and published by Springer. This book was released on 2004-10-23 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
Book Synopsis Geometric Mechanics by : Darryl D. Holm
Download or read book Geometric Mechanics written by Darryl D. Holm and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symplectic Geometry and Topology by : Yakov Eliashberg
Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Book Synopsis Mathematical Methods of Classical Mechanics by : V.I. Arnol'd
Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Book Synopsis Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) by : Holm Darryl D
Download or read book Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) written by Holm Darryl D and published by World Scientific. This book was released on 2011-10-31 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Geometric Optics on Phase Space by : Kurt Bernardo Wolf
Download or read book Geometric Optics on Phase Space written by Kurt Bernardo Wolf and published by Springer Science & Business Media. This book was released on 2004-07-21 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.
