Nonlinear Mechanics, Groups and Symmetry
Author: Yuri A. Mitropolsky
Publisher: Springer
Published: 2012-12-22
Total Pages: 382
ISBN-13: 9789401585361
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Nonlinear Mechanics, Groups and Symmetry
Author: Юрий Алексеевич Митропольский
Publisher: Springer
Published: 1995-01-31
Total Pages: 400
ISBN-13:
DOWNLOAD EBOOK →This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
Nonlinear Mechanics, Groups and Symmetry
Author: Yuri A. Mitropolsky
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 391
ISBN-13: 9401585350
DOWNLOAD EBOOK →This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
Introduction to Mechanics and Symmetry
Author: Jerrold E. Marsden
Publisher: Springer Science & Business Media
Published: 2013-03-19
Total Pages: 593
ISBN-13: 0387217924
DOWNLOAD EBOOK →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.
Applied Mechanics Reviews
Group-Theoretic Methods in Mechanics and Applied Mathematics
Author: D.M. Klimov
Publisher: CRC Press
Published: 2014-04-21
Total Pages: 240
ISBN-13: 1482265222
DOWNLOAD EBOOK →Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. Symmetries and conservat
Symmetries and Applications of Differential Equations
Author: Albert C. J. Luo
Publisher: Springer Nature
Published: 2021-12-14
Total Pages: 287
ISBN-13: 981164683X
DOWNLOAD EBOOK →This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939–2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.
Similarity and Symmetry Methods
Author: Jean-François Ganghoffer
Publisher: Springer
Published: 2014-07-19
Total Pages: 380
ISBN-13: 3319082965
DOWNLOAD EBOOK →The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint. The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.
Geometric Mechanics and Symmetry
Author: Darryl D. Holm
Publisher: Oxford University Press
Published: 2009-07-30
Total Pages:
ISBN-13: 0191549878
DOWNLOAD EBOOK →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.
Imperfect Bifurcation in Structures and Materials
Author: Kiyohiro Ikeda
Publisher: Springer Nature
Published: 2019-09-25
Total Pages: 590
ISBN-13: 3030214737
DOWNLOAD EBOOK →Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.
