Geometric Mechanics And Symmetry PDF Download
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| Author | : Darryl D. Holm |
| Publisher | : Oxford University Press |
| Total Pages | : |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 0191549878 |
Download Geometric Mechanics and Symmetry Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 593 |
| Release | : 2013-03-19 |
| Genre | : Science |
| ISBN | : 0387217924 |
Download Introduction to Mechanics and Symmetry Book in PDF, ePub and Kindle
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 | : Darryl D. Holm |
| Publisher | : Oxford University Press |
| Total Pages | : 537 |
| Release | : 2009-07-30 |
| Genre | : Mathematics |
| ISBN | : 0199212902 |
Download Geometric Mechanics and Symmetry Book in PDF, ePub and Kindle
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 | : Stephanie Frank Singer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 201 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201896 |
Download Symmetry in Mechanics Book in PDF, ePub and Kindle
"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 | : James Montaldi |
| Publisher | : Cambridge University Press |
| Total Pages | : 416 |
| Release | : 2005-05-05 |
| Genre | : Mathematics |
| ISBN | : 9780521539579 |
Download Geometric Mechanics and Symmetry Book in PDF, ePub and Kindle
The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.
| Author | : Holm Darryl D |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 468 |
| Release | : 2011-07-13 |
| Genre | : Mathematics |
| ISBN | : 1911298658 |
Download Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) Book in PDF, ePub and Kindle
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 | : Jerrold E. Marsden |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1992-04-30 |
| Genre | : Mathematics |
| ISBN | : 9780521428446 |
Download Lectures on Mechanics Book in PDF, ePub and Kindle
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.
| Author | : R. McWeeny |
| Publisher | : Elsevier |
| Total Pages | : 263 |
| Release | : 2013-09-03 |
| Genre | : Mathematics |
| ISBN | : 1483226247 |
Download Symmetry Book in PDF, ePub and Kindle
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 | : Kurt Bernardo Wolf |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 400 |
| Release | : 2004-07-21 |
| Genre | : Science |
| ISBN | : 9783540220398 |
Download Geometric Optics on Phase Space Book in PDF, ePub and Kindle
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.
| Author | : Francesco Bullo |
| Publisher | : Springer |
| Total Pages | : 727 |
| Release | : 2019-06-12 |
| Genre | : Science |
| ISBN | : 1489972765 |
Download Geometric Control of Mechanical Systems Book in PDF, ePub and Kindle
The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.
