Geometric Mechanics Dynamics And Symmetry

Author : Holm Darryl D
Publisher : World Scientific Publishing Company
Page : 468 pages
File Size : 42,7 Mb
Release : 2011-07-13
Category : Mathematics
ISBN : 9781911298656

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Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) by Holm Darryl D Pdf

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 : Darryl D. Holm,Tanya Schmah,Cristina Stoica
Publisher : Oxford University Press
Page : 128 pages
File Size : 42,6 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 : Darryl D. Holm,Tanya Schmah,Cristina Stoica
Publisher : Oxford University Press
Page : 537 pages
File Size : 49,8 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780199212903

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

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 : Darryl D. Holm
Publisher : Imperial College Press
Page : 375 pages
File Size : 49,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9781848161955

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Geometric Mechanics: Dynamics and symmetry by Darryl D. Holm Pdf

Advanced undergraduate and graduate students in mathematics, physics and engineering.

Author : Darryl D Holm
Publisher : World Scientific Publishing Company
Page : 311 pages
File Size : 42,5 Mb
Release : 2008-04-14
Category : Mathematics
ISBN : 9781911299332

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Geometric Mechanics by Darryl D Holm Pdf

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.

Author : James Montaldi,Tudor Ratiu
Publisher : Cambridge University Press
Page : 416 pages
File Size : 44,9 Mb
Release : 2005-05-05
Category : Mathematics
ISBN : 0521539579

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Geometric Mechanics and Symmetry by James Montaldi,Tudor Ratiu Pdf

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 : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Page : 593 pages
File Size : 53,7 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 : Holm Darryl D
Publisher : World Scientific
Page : 412 pages
File Size : 51,9 Mb
Release : 2011-10-31
Category : Mathematics
ISBN : 9781911298663

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Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2nd Edition) by Holm Darryl D Pdf

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

Author : James Montaldi,Tudor S. Ratiu
Publisher : Unknown
Page : 128 pages
File Size : 42,9 Mb
Release : 2005
Category : Electronic
ISBN : 1139882120

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Peyresq Lectures on Geometric Mechanics and Symmetry by James Montaldi,Tudor S. Ratiu Pdf

Author : Jerrold E. Marsden
Publisher : Cambridge University Press
Page : 272 pages
File Size : 50,7 Mb
Release : 1992-04-30
Category : Mathematics
ISBN : 0521428440

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Lectures on Mechanics by Jerrold E. Marsden Pdf

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 : Darryl D. Holm
Publisher : Imperial College Press
Page : 311 pages
File Size : 42,7 Mb
Release : 2008
Category : Science
ISBN : 9781848161559

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Geometric Mechanics: Rotating, translating and rolling by Darryl D. Holm Pdf

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.

Author : Carl Wulfman
Publisher : World Scientific
Page : 459 pages
File Size : 51,8 Mb
Release : 2011
Category : Science
ISBN : 9789814291361

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Dynamical Symmetry by Carl Wulfman Pdf

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.

Author : Kurt Bernardo Wolf
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 43,6 Mb
Release : 2004-07-21
Category : Science
ISBN : 3540220399

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Geometric Optics on Phase Space by Kurt Bernardo Wolf Pdf

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 : Waldyr Muniz Oliva
Publisher : Springer
Page : 276 pages
File Size : 40,6 Mb
Release : 2004-10-25
Category : Science
ISBN : 9783540457954

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Geometric Mechanics by Waldyr Muniz Oliva Pdf

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.

Author : Taeyoung Lee,Melvin Leok,N. Harris McClamroch
Publisher : Springer
Page : 539 pages
File Size : 45,9 Mb
Release : 2017-08-14
Category : Mathematics
ISBN : 9783319569536

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Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by Taeyoung Lee,Melvin Leok,N. Harris McClamroch Pdf

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.