Rotation, Reflection, and Frame Changes is an engineer's practical resource for rotation-related theorems that might otherwise be difficult to find in the literature. By providing extensive tutorials in requisite mathematics, intuitive insight, and computer source code, this work stands as a definitive contribution to engineering mechanics.
A bestselling textbook in its first three editions, Continuum Mechanics for Engineers, Fourth Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. It provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. Through a mastery of this volume’s contents and additional rigorous finite element training, readers will develop the mechanics foundation necessary to skillfully use modern, advanced design tools. Features: Provides a basic, understandable approach to the concepts, mathematics, and engineering applications of continuum mechanics Updated throughout, and adds a new chapter on plasticity Features an expanded coverage of fluids Includes numerous all new end-of-chapter problems With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills.
Almost all materials are inhomogeneous at the microscale. Typical examples are fiber- and grain structures made of anisotropic phases. These cannot be accounted for in detail in engineering calculations. Instead, effective, homogeneous material properties are used. These are obtained from the inhomogeneous structures by homogenization methods. This book provides a structured overview of the analytical homogenization methods, including the most common estimates, bounds, and Fourier methods. The focus is on linear and anisotropic constitutive relationships, like Hookean elasticity and Fourier’s law for thermal conduction. All sections are accompanied by example calculations, including program code that is also available online.
The first two chapters of the book deal, in a detailed way, with relativistic kinematics and dynamics, while in the third chapter some elementary concepts of General Relativity are given. Eventually, after an introduction to tensor calculus, a Lorentz covariant formulation of electromagnetism is given its quantization is developed. For a proper treatment of invariance and conservation laws in physics, an introductory chapter on group theory is given. This introduction is propedeutical to the discussion of conservation laws in the Lagrangian and Hamiltonian formalism, which will allow us to export this formalism to quantum mechanics and, in particular, to introduce linear operators on quantum states and their transformation laws. In the last part of the book we analyze, in the first quantized formalism, relativistic field theory for both boson and fermion fields. The second quantization of free fields is then introduced and some preliminary concepts of perturbation theory and Feynmann diagrams are given and some relevant examples are worked out.
Dispersed multiphase flows are frequently found in nature and have diverse geophysical, environmental, industrial, and energy applications. This book targets a beginning graduate student looking to learn about the physical processes that govern these flows, going from the fundamentals to the state of the art, with many exercises included.
Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. The geometry is limited to the Euclidean space/geometry, where the Pythagorean Theorem applies, with well-defined Cartesian coordinate systems as the reference. Quantities defined in curvilinear coordinate systems, like cylindrical, spherical, parabolic, etc. are discussed and several examples and coordinates sketches with related calculations are presented. In addition, the book has several worked-out examples for helping readers with mastering the topics provided in the prior sections. FEATURES: Expanded content on the rigid body rotation and Cartesian tensors by including Euler angles and quaternion methods Easy to understand mathematical concepts through numerous figures, solved examples, and exercises List of gradient-like operators for major systems of coordinates.
This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.
In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.
Physics owes much of its success to the application of differential calculus. Correspondingly, most laws of physics are formulated as differential equations. This success has created the prejudice that a science cannot be ‘exact’ unless it stands firmly on a foundation of calculus. This doesn’t, however, work for biology. Living things are not as continuous, let alone differentiable, as most organisms and their parts change or end quite abruptly. Biology cannot offer differential equations for (say) the role of chromosomal telomeres in aging, or a link between macrophage polyploidy and cancer. The information flow between the limbic system and the frontal cortex is far too erratic to permit differentiation. The pheromone secretions that control the social order of ants follow no mathematical laws. The topology of the human skeleton is neither a perfect sphere, nor an idealized doughnut. However, all these and countless other biological phenomena decide life and death and are amazingly exact As such, instead of even trying to paint living things with the exquisitely resolving brush of differential calculus, we may accept that they are actually made up of individual and sizable ‘pixels’. Hence, this book presents a novel view of biology as the unified science of ‘living mosaics’, which consist of discrete, yet interacting, ‘tiles’, which, in turn, are such ‘mosaics’ in their own rights.
