Cartesian Tensors in Engineering Science: The Commonwealth and International Library: Structures and Solid Body Mechanics Division by L. G. Jaeger (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book serves as an excellent introduction to tensors for the student. It generalises all physical quantities into tensor form (e.g. a scalar is a zeroth order tensor, a vector is a first order tensor, etc.) It provides a clear treatise on directional cosines, transformation of tensors, symmetric second order tensors, tensor products, and then two aspplications, namely elasticity and dynamics. For anyone wishing to understand the nature of Cartesian tensors, their notation, and computation, this book is a must.

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