Symmetry in Applied Continuous Mechanics

Symmetry in Applied Continuous Mechanics PDF Author: Marin Marin
Publisher:
ISBN: 9783039430307
Category :
Languages : en
Pages : 232

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Book Description
Engineering practice requires the use of structures containing identical components or parts, useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analyses of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Machine building, automotive, aerospace, and civil engineering are the main areas in which such applications appear, but they are found in most engineering fields.

Symmetry in Applied Continuous Mechanics

Symmetry in Applied Continuous Mechanics PDF Author: Marin Marin
Publisher:
ISBN: 9783039430307
Category :
Languages : en
Pages : 232

Get Book Here

Book Description
Engineering practice requires the use of structures containing identical components or parts, useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analyses of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Machine building, automotive, aerospace, and civil engineering are the main areas in which such applications appear, but they are found in most engineering fields.

Similarity and Symmetry Methods

Similarity and Symmetry Methods PDF Author: Jean-François Ganghoffer
Publisher: Springer
ISBN: 3319082965
Category : Science
Languages : en
Pages : 380

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Book Description
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.

Introduction to Mechanics and Symmetry

Introduction to Mechanics and Symmetry PDF Author: Jerrold E. Marsden
Publisher: Springer Science & Business Media
ISBN: 0387217924
Category : Science
Languages : en
Pages : 593

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Book Description
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.

Introduction to Continuous Symmetries

Introduction to Continuous Symmetries PDF Author: Franck Laloë
Publisher: John Wiley & Sons
ISBN: 3527414169
Category : Science
Languages : en
Pages : 581

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Book Description
In dem neuen Werk von Franck Laloe wird ein symmetriebasierter Ansatz zum grundlegenden Verständnis der Quantenmechanik vorgestellt ? zusammen mit den entsprechenden Rechentechniken, die Studierende höherer Semester in den Bereichen Nuklearphysik, Quantenopik und Festkörperphysik benötigen.

Dynamical Symmetry

Dynamical Symmetry PDF Author: Carl Wulfman
Publisher: World Scientific
ISBN: 9814291366
Category : Science
Languages : en
Pages : 459

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Book Description
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.

Symmetry in Complex Network Systems

Symmetry in Complex Network Systems PDF Author: Visarath In
Publisher: Springer
ISBN: 366255545X
Category : Technology & Engineering
Languages : en
Pages : 406

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Book Description
This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.

Dynamical Symmetry

Dynamical Symmetry PDF Author: Carl E Wulfman
Publisher: World Scientific
ISBN: 9814466115
Category : Science
Languages : en
Pages : 459

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Book Description
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.

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry PDF Author: Darryl D. Holm
Publisher: Oxford University Press
ISBN: 0191549878
Category : Mathematics
Languages : en
Pages :

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Book Description
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.

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry PDF Author: Darryl D. Holm
Publisher: Oxford University Press
ISBN: 0199212902
Category : Mathematics
Languages : en
Pages : 537

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Book Description
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.

Symmetries in Physics

Symmetries in Physics PDF Author: Wolfgang Ludwig
Publisher: Springer Science & Business Media
ISBN: 364297029X
Category : Science
Languages : en
Pages : 471

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Book Description
Everyone knows that symmetry is fundamentally important in physics. On one hand, the symmetry of a system is often the starting point for general physical considerations, and on the other hand, particular problems may be solved in simpler and more elegant ways if symmetry is taken into account. This book presents the underlying theories of symmetry and gives examples of their application in branches of physics ranging from solid-state to high-energy physics via atomic and molecular physics. The text is as self-contained as possible, with as much mathematical formalism given as required. The main emphasis is on the theory of group representations and on the method of projection operators, this is a very powerful tool which is often treated only very briefly. Discrete symmetries, continuous symmetries and symmetry breaking are also discussed, and exercises are provided to stimulate the reader to carry out original work.