Download or read book Cartesian Tensors in Engineering Science written by L. G. Jaeger and published by Elsevier. This book was released on 2016-06-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cartesian Tensors in Engineering Science written by Leslie Gordon JAEGER and published by Pergamon. This book was released on 1966-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Vectors and Cartesian Tensors written by Richard E. Haskell and published by Prentice Hall. This book was released on 1972 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cartesian Tensors written by George Frederick James Temple and published by Courier Corporation. This book was released on 2004-09-01 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of Cartesian tensors, this text notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. Covers isotropic tensors and spinor analysis within the confines of Euclidean space; and tensors in orthogonal curvilinear coordinates. Examples. 1960 edition.
Download or read book An Introduction to Tensor Analysis written by Bipin Singh Koranga and published by CRC Press. This book was released on 2022-09-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vector Analysis and Cartesian Tensors written by D. E. Bourne and published by Academic Press. This book was released on 2014-05-10 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.
Download or read book An Introduction to Tensor Analysis for Engineers and Applied Scientists written by John R. Tyldesley and published by Longman Publishing Group. This book was released on 1975 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Analysis and Cartesian Tensors written by Donald Edward Bourne and published by CRC Press. This book was released on 2018-05-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive self-contained text suitable for use by undergraduate mathematics, science and engineering students following courses in vector analysis. The earlier editions have been used extensively in the design and teaching of may undergraduate courses. Vectors are introduced in terms of Cartesian components, an approach which is found to appeal to many students because of the basic algebraic rules of composition of vectors and the definitions of gradient divergence and curl are thus made particularly simple. The theory is complete, and intended to be as rigorous as possible at the level at which it is aimed.
Download or read book Cartesian Tensors written by Nils O. Myklestad and published by Princeton, N.J : Van Nostrand. This book was released on 1967 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Analysis and Cartesian Tensors Third edition written by P C Kendall and published by Routledge. This book was released on 2017-09-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.
Download or read book Cartesian tensors and the equations of solid mechanics written by K. B. M. Nambudiripad and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Elasticity written by J D Renton and published by Elsevier. This book was released on 2002-12-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. - Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987 - Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approach - Uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis
Download or read book Cartesian Tensors written by Harold Jeffreys and published by . This book was released on 1961 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Analysis and Cartesian Tensors written by Donald Edward Bourne and published by . This book was released on 1977 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.
Download or read book Cartesian Tensors written by G. Temple and published by Courier Corporation. This book was released on 2012-05-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate-level text provides an introduction to isotropic tensors and spinor analysis, with numerous examples that illustrate the general theory and indicate certain extensions and applications. 1960 edition.
Download or read book Tensor Analysis for Engineers written by Mehrzad Tabatabaian and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensors for Physics written by Siegfried Hess and published by Springer. This book was released on 2015-04-25 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.
