Introduction To Mechanics And Symmetry

Author : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Page : 593 pages
File Size : 45,8 Mb
Release : 2013-03-19
Category : Science
ISBN : 9780387217925

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Introduction to Mechanics and Symmetry by Jerrold E. Marsden,Tudor S. Ratiu Pdf

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 : J.E. Marsden,Tudor Ratiu
Publisher : Springer
Page : 586 pages
File Size : 51,9 Mb
Release : 2013-02-02
Category : Science
ISBN : 1475755872

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Introduction to Mechanics and Symmetry by J.E. Marsden,Tudor Ratiu Pdf

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 : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer
Page : 0 pages
File Size : 49,5 Mb
Release : 1994-12-13
Category : Science
ISBN : 1461226821

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Introduction to Mechanics and Symmetry by Jerrold E. Marsden,Tudor S. Ratiu Pdf

Mathematics is playing an ever more important role in the physical and biological sciences. provoking a blurring of boundaries between scientific dis ciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathe matics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Siiences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface Symmetry and mechanics have been close partners since the time of the founding masters, namely, Newton, Euler, Lagrange, Laplace, Poisson, Ja cobi, and Hamilton, and its subsequent developers, including Noether, Rie mann, Routh, Kelvin, Poincare, and Cartan. To this day, symmetry has continued to playa strong role, especially with the modern work of Arnold, Guillemin, Kirillov, Kostant, Moser, Smale, Souriau, Sternberg, and many others.

Author : Stephanie Frank Singer
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201892

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Symmetry in Mechanics by Stephanie Frank Singer Pdf

"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 : Darryl D. Holm,Tanya Schmah,Cristina Stoica
Publisher : Oxford University Press
Page : 128 pages
File Size : 52,6 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780191549878

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Geometric Mechanics and Symmetry by Darryl D. Holm,Tanya Schmah,Cristina Stoica Pdf

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 : Jerrold E. Marsden,Tudor S. Rațiu,Juan-Pablo Ortega
Publisher : Unknown
Page : 352 pages
File Size : 41,9 Mb
Release : 1996
Category : Mechanics, Analytic
ISBN : OCLC:36670690

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Introduction to Mechanics and Symmetry by Jerrold E. Marsden,Tudor S. Rațiu,Juan-Pablo Ortega Pdf

Author : Scott Corry
Publisher : CRC Press
Page : 177 pages
File Size : 55,7 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9781315354606

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Symmetry and Quantum Mechanics by Scott Corry Pdf

Structured as a dialogue between a mathematician and a physicist, Symmetry and Quantum Mechanics unites the mathematical topics of this field into a compelling and physically-motivated narrative that focuses on the central role of symmetry. Aimed at advanced undergraduate and beginning graduate students in mathematics with only a minimal background in physics, this title is also useful to physicists seeking a mathematical introduction to the subject. Part I focuses on spin, and covers such topics as Lie groups and algebras, while part II offers an account of position and momentum in the context of the representation theory of the Heisenberg group, along the way providing an informal discussion of fundamental concepts from analysis such as self-adjoint operators on Hilbert space and the Stone-von Neumann Theorem. Mathematical theory is applied to physical examples such as spin-precession in a magnetic field, the harmonic oscillator, the infinite spherical well, and the hydrogen atom.

Author : John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss
Publisher : CRC Press
Page : 442 pages
File Size : 47,7 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781439864890

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The Symmetries of Things by John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss Pdf

Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

Author : R. McWeeny
Publisher : Elsevier
Page : 262 pages
File Size : 47,9 Mb
Release : 2013-09-03
Category : Mathematics
ISBN : 9781483226248

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Symmetry by R. McWeeny Pdf

Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Author : Jakob Schwichtenberg
Publisher : Springer
Page : 287 pages
File Size : 40,7 Mb
Release : 2017-12-01
Category : Science
ISBN : 9783319666310

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Physics from Symmetry by Jakob Schwichtenberg Pdf

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.

Author : Walter Greiner,Berndt Müller
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579769

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Quantum Mechanics by Walter Greiner,Berndt Müller Pdf

Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.

Author : Brian Cantwell
Publisher : Cambridge University Press
Page : 660 pages
File Size : 54,9 Mb
Release : 2002-09-23
Category : Mathematics
ISBN : 0521777402

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Introduction to Symmetry Analysis Paperback with CD-ROM by Brian Cantwell Pdf

An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.

Author : Daniel Kleppner,Robert Kolenkow
Publisher : Cambridge University Press
Page : 563 pages
File Size : 40,7 Mb
Release : 2014
Category : Science
ISBN : 9780521198110

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An Introduction to Mechanics by Daniel Kleppner,Robert Kolenkow Pdf

This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.

Author : Lev V. Prokhorov,Sergei V. Shabanov
Publisher : Cambridge University Press
Page : 485 pages
File Size : 44,6 Mb
Release : 2011-09-22
Category : Science
ISBN : 9781139500906

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Hamiltonian Mechanics of Gauge Systems by Lev V. Prokhorov,Sergei V. Shabanov Pdf

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Author : Ian Stewart
Publisher : OUP Oxford
Page : 152 pages
File Size : 44,5 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9780191652745

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Symmetry: A Very Short Introduction by Ian Stewart Pdf

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.