Geometry Symmetries And Classical Physics

Author : Manousos Markoutsakis
Publisher : CRC Press
ISBN 13 : 1000530248
Total Pages : 482 pages
Book Rating : 4.47/5 ( download)

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Download or read book Geometry, Symmetries, and Classical Physics written by Manousos Markoutsakis and published by CRC Press. This book was released on 2021-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique

Author : Manousos Markoutsakis
Publisher : CRC Press
ISBN 13 : 1000530264
Total Pages : 702 pages
Book Rating : 4.61/5 ( download)

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Download or read book Geometry, Symmetries, and Classical Physics written by Manousos Markoutsakis and published by CRC Press. This book was released on 2021-12-29 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique

Author : Darryl D. Holm
Publisher : Oxford University Press
ISBN 13 : 0191549878
Total Pages : pages
Book Rating : 4.78/5 ( download)

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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 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Darryl D. Holm
Publisher : Oxford University Press
ISBN 13 : 0199212902
Total Pages : 537 pages
Book Rating : 4.03/5 ( download)

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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.

Author : Holm Darryl D
Publisher : World Scientific Publishing Company
ISBN 13 : 1911298658
Total Pages : 468 pages
Book Rating : 4.56/5 ( download)

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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

Author : Stephanie Frank Singer
Publisher : Springer Science & Business Media
ISBN 13 : 1461201896
Total Pages : 201 pages
Book Rating : 4.92/5 ( download)

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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.

Author : Klaus Mainzer
Publisher : Walter de Gruyter
ISBN 13 : 3110886936
Total Pages : 696 pages
Book Rating : 4.31/5 ( download)

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Download or read book Symmetries of Nature written by Klaus Mainzer and published by Walter de Gruyter. This book was released on 2013-12-02 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jerrold E. Marsden
Publisher : Springer Science & Business Media
ISBN 13 : 0387217924
Total Pages : 593 pages
Book Rating : 4.25/5 ( download)

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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.

Author : Kai S Lam
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107480
Total Pages : 460 pages
Book Rating : 4.89/5 ( download)

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Download or read book Non-Relativistic Quantum Theory written by Kai S Lam and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 460 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.

Author : Jakob Schwichtenberg
Publisher : Springer
ISBN 13 : 3319666312
Total Pages : 287 pages
Book Rating : 4.10/5 ( download)

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Download or read book Physics from Symmetry written by Jakob Schwichtenberg and published by Springer. This book was released on 2017-12-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.