A Note On Physical Components Of Tensors
DOWNLOAD
Download A Note On Physical Components Of Tensors PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Note On Physical Components Of Tensors book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Physical Components Of Tensors
DOWNLOAD
Author : Wolf Altman
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Physical Components Of Tensors written by Wolf Altman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory of physical and anholonomic components of tensors and applies the theory of dimensional analysis to tensors and (anholonomic) connections. This theory shows the relationship and compatibility among several existing definitions of physical components of tensors when referred to nonorthogonal coordinates. The book assumes a basic knowledge of linear algebra and elementary calculus, but revisits these subjects and introduces the mathematical backgrounds for the theory in the first three chapters. In addition, all field equations are also given in physical components as well. Comprised of five chapters, this noteworthy text: Deals with the basic concepts of linear algebra, introducing the vector spaces and the further structures imposed on them by the notions of inner products, norms, and metrics Focuses on the main algebraic operations for vectors and tensors and also on the notions of duality, tensor products, and component representation of tensors Presents the classical tensor calculus that functions as the advanced prerequisite for the development of subsequent chapters Provides the theory of physical and anholonomic components of tensors by associating them to the spaces of linear transformations and of tensor products and advances two applications of this theory Physical Components of Tensors contains a comprehensive account of tensor calculus, and is an essential reference for graduate students or engineers concerned with solid and structural mechanics.
A Note On Physical Components Of Tensors
DOWNLOAD
Author : Luigi Morino
language : en
Publisher:
Release Date : 1972
A Note On Physical Components Of Tensors written by Luigi Morino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Shells (Engineering) categories.
Polyadics And Physical Components Of Tensors
DOWNLOAD
Author : Kent Gardner Stansberry
language : en
Publisher:
Release Date : 1967
Polyadics And Physical Components Of Tensors written by Kent Gardner Stansberry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Calculus of tensors categories.
An Introduction To Tensor Calculus
DOWNLOAD
Author : Jacques L. Mercier
language : en
Publisher:
Release Date : 1971
An Introduction To Tensor Calculus written by Jacques L. Mercier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Calculus of tensors categories.
A Brief On Tensor Analysis
DOWNLOAD
Author : J.G. Simmonds
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Brief On Tensor Analysis written by J.G. Simmonds and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
When I was an undergraduate, working as a co-op student at North American Aviation, I tried to learn something about tensors. In the Aeronautical En gineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a tum-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor. Tensor-what power those two syllables seemed to resonate. I had heard the word once before, in an aside by a graduate instructor to the cognoscenti in the front row of a course in strength of materials. "What the book calls stress is actually a tensor. . . ." With my interest twice piqued and with time off from fighting the brush fires of a demanding curriculum, I was ready for my first serious effort at self instruction. In Los Angeles, after several tries, I found a store with a book on tensor analysis. In my mind I had rehearsed the scene in which a graduate stu dent or professor, spying me there, would shout, "You're an undergraduate.
An Introduction To Tensor Analysis
DOWNLOAD
Author : Bipin Singh Koranga
language : en
Publisher: CRC Press
Release Date : 2022-09-01
An Introduction To Tensor Analysis written by Bipin Singh Koranga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Mathematics categories.
The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.
Physical Applications Of Vectors And Tensors
DOWNLOAD
Author : Horst Teichmann
language : en
Publisher:
Release Date : 1969
Physical Applications Of Vectors And Tensors written by Horst Teichmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Calculus of tensors categories.
Tensor Analysis
DOWNLOAD
Author : Fridtjov Irgens
language : en
Publisher: Springer
Release Date : 2018-12-15
Tensor Analysis written by Fridtjov Irgens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-15 with Science categories.
This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers. The discussion is based on the concepts of vectors and vector analysis in three-dimensional Euclidean space, and although it takes the subject matter to an advanced level, the book starts with elementary geometrical vector algebra so that it is suitable as a first introduction to tensors and tensor analysis. Each chapter includes a number of problems for readers to solve, and solutions are provided in an Appendix at the end of the text. Chapter 1 introduces the necessary mathematical foundations for the chapters that follow, while Chapter 2 presents the equations of motions for bodies of continuous material. Chapter 3 offers a general definition of tensors and tensor fields in three-dimensional Euclidean space. Chapter 4 discusses a new family of tensors related to the deformation of continuous material. Chapter 5 then addresses constitutive equations for elastic materials and viscous fluids, which are presented as tensor equations relating the tensor concept of stress to the tensors describing deformation, rate of deformation and rotation. Chapter 6 investigates general coordinate systems in three-dimensional Euclidean space and Chapter 7 shows how the tensor equations discussed in chapters 4 and 5 are presented in general coordinates. Chapter 8 describes surface geometry in three-dimensional Euclidean space, Chapter 9 includes the most common integral theorems in two- and three-dimensional Euclidean space applied in continuum mechanics and mathematical physics.
Tensor Analysis And Nonlinear Tensor Functions
DOWNLOAD
Author : Yuriy I. Dimitrienko
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Tensor Analysis And Nonlinear Tensor Functions written by Yuriy I. Dimitrienko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.
Cartesian Tensors In Engineering Science
DOWNLOAD
Author : L. G. Jaeger
language : en
Publisher: Elsevier
Release Date : 2015-09-03
Cartesian Tensors In Engineering Science written by L. G. Jaeger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Technology & Engineering categories.
Cartesian Tensors in Engineering Science provides a comprehensive discussion of Cartesian tensors. The engineer, when working in three dimensions, often comes across quantities which have nine components. Variation of the components in a given plane may be shown graphically by a familiar construction called Mohr's circle. For such quantities it is always possible to find three mutually perpendicular axes, called principal axes, with respect to which the six ""paired up"" components are all zero. Such quantities are called symmetric tensors of the second order. The student may at this stage be struck by the fact that the physical quantities with which he normally deals have either one component, three components or nine components, being respectively scalars, vectors, and what have just been called second order tensors. The family of quantities having 1, 3, 9, 27, ... components does exist. It is the tensor family in three dimensions. The book discusses the ""tests"" a given quantity must pass in order to qualify as a member of the family. The products of tensors, elasticity, and second moment of area and moment of inertia are also covered. Although written primarily for engineers, it is hoped that students of various branches of physical science may find this book useful.