**Author**: Patrick Hamill

**Publisher:** Cambridge University Press

**ISBN:**

**Category:** Science

**Page:** 184

**View:** 464

A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.

Vectors, tensors and functions -- Manifolds, vectors and differentiation -- Energy, momentum and Einstein's equations

An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.

This book takes the student from the Newtonian mechanics typically taught in the first and the second year to the areas of recent research. The discussion of topics such as invariance, Hamiltonian-Jacobi theory, and action-angle variables is especially complete; the last includes a discussion of the Hannay angle, not found in other texts. The final chapter is an introduction to the dynamics of nonlinear nondissipative systems. Connections with other areas of physics which the student is likely to be studying at the same time, such as electromagnetism and quantum mechanics, are made where possible. There is thus a discussion of electromagnetic field momentum and mechanical?hidden? momentum in the quasi-static interaction of an electric charge and a magnet. This discussion, among other things explains the?(e/c)A? term in the canonical momentum of a charged particle in an electromagnetic field. There is also a brief introduction to path integrals and their connection with Hamilton's principle, and the relation between the Hamilton-Jacobi equation of mechanics, the eikonal equation of optics, and the Schrdinger equation of quantum mechanics.The text contains 115 exercises. This text is suitable for a course in classical mechanics at the advanced undergraduate level.

Nanooptics which describes the interaction of light with matter at the nanoscale, is a topic of great fundamental interest to physicists and engineers and allows the direct observation of quantum mechanical phenomena in action. This self-contained and extensively referenced text describes the underlying theory behind nanodevices operating in the quantum regime for use both in advanced courses and as a reference for researchers in physics, chemistry, electrical engineering, and materials science. Presenting an extensive theoretical toolset for design and analysis of nanodevices, the authors demonstrate the art of developing approximate quantum models of real nanodevices. The rudimentary mathematical knowledge required to master the material is carefully introduced, with detailed derivations and frequent worked examples allowing readers to gain a thorough understanding of the material. More advanced applications are gradually introduced alongside analytical approximations and simplifying assumptions often used to make such problems tractable while representative of the observed features.

Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, rather than the rather startling differences.

Chrology was conducted in various and generalize domain to catch all universe and his presence in one law. Over eighteen years of quest, these researches open a huge door to Rotam to discover a single and absolute law that governs all presence and existence of Universe. Chrology is the science of all sciences, unification of all human knowledge and show the whole universe in its different faces of existence. Chrology explain everything that the entire system of the universe allows us to access, understand that escape our standard methods. Chrology opens up a new conception and new ideas to add to our knowledge to understand how the absolute mysteries, the immeasurable beauties and the complexities of the universe must present itself to our access with a unique law.

In Physics, Structure, and Reality, Jill North addresses a set of questions that get to the heart of the project of interpreting physics—of figuring out what physics is telling us about the world. How do we figure out the nature of the world from a mathematically formulated physical theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? North argues that there is a certain notion of structure, implicit in physics and mathematics, to which we should pay careful attention in order to discern what physics is telling us about the nature of reality. North draws lessons for related topics, including the use of coordinate systems in physics, the differences among various formulations of classical mechanics, the nature of spacetime structure, the equivalence of physical theories, and the importance of scientific explanation. Although the book does not explicitly defend scientific realism, instead taking this to be a background assumption, the account provides an indirect case for realism toward our best theories of physics.

The book focuses on smart computing for crowdfunding usage, looking at the crowdfunding landscape, e.g., reward-, donation-, equity-, P2P-based and the crowdfunding ecosystem, e.g., regulator, asker, backer, investor, and operator. The increased complexity of fund raising scenario, driven by the broad economic environment as well as the need for using alternative funding sources, has sparked research in smart computing techniques. Covering a wide range of detailed topics, the authors of this book offer an outstanding overview of the current state of the art; providing deep insights into smart computing methods, tools, and their applications in crowdfunding; exploring the importance of smart analysis, prediction, and decision-making within the fintech industry. This book is intended to be an authoritative and valuable resource for professional practitioners and researchers alike, as well as finance engineering, and computer science students who are interested in crowdfunding and other emerging fintech topics.

This course-based text revisits classic concepts in nonlinear circuit theory from a very much introductory point of view: the presentation is completely self-contained and does not assume any prior knowledge of circuit theory. It is simply assumed that readers have taken a first-year undergraduate course in differential and integral calculus, along with an elementary physics course in classical mechanics and electrodynamics. Further, it discusses topics not typically found in standard textbooks, such as nonlinear operational amplifier circuits, nonlinear chaotic circuits and memristor networks. Each chapter includes a set of illustrative and worked examples, along with end-of-chapter exercises and lab exercises using the QUCS open-source circuit simulator. Solutions and other material are provided on the YouTube channel created for this book by the authors.

Rotordynamics of automotive turbochargers is dealt with in this book encompassing the widely working field of small turbomachines under real operating conditions at the very high rotor speeds up to 300000 rpm. The broadly interdisciplinary field of turbocharger rotordynamics involves 1) Thermodynamics and Turbo-Matching of Turbochargers 2) Dynamics of Turbomachinery 3) Stability Analysis of Linear Rotordynamics with the Eigenvalue Theory 4) Stability Analysis of Nonlinear Rotordynamics with the Bifurcation Theory 5) Bearing Dynamics of the Oil Film using the Two-Phase Reynolds Equation 6) Computation of Nonlinear Responses of a Turbocharger Rotor 7) Aero and Vibroacoustics of Turbochargers 8) Shop and Trim Balancing at Two Planes of the Rotor 9) Tribology of the Bearing Surface Roughness 10) Design of Turbocharger Platforms using the Similarity Laws The rotor response of an automotive turbocharger at high rotor speeds is studied analytically, computationally, and experimentally. Due to the nonlinear characteristics of the oil-film bearings, some nonlinear responses of the rotor besides the harmonic response 1X, such as oil whirl, oil whip, and modulated frequencies occur in Waterfall diagram. Additionally, the influences of the surface roughness and oil characteristics on the rotor behavior, friction, and wear are discussed. This book is written by an industrial R&D expert with many years of experience in the automotive and turbocharger industries. The all-in-one book of turbochargers is intended for scientific and engineering researchers, practitioners working in the rotordynamics field of automotive turbochargers, and graduate students in applied physics and mechanical engineering.

A volcanic eruption occurs when a magma-filled fracture propagates from its source to the surface. Analysing and understanding the conditions that allow this to happen constitute a major part of the scientific field of volcanotectonics. This new volume introduces this cutting-edge and interdisciplinary topic in volcanological research, which incorporates principles and methods from structural geology, tectonics, volcano-deformation studies, physical volcanology, seismology, and physics. It explains and illustrates the physical processes that operate inside volcanoes and which control the frequencies, locations, durations, and sizes of volcanic eruptions. Featuring a clear theoretical framework and helpful summary descriptions of various volcanic structures and products, as well as many worked examples and exercises, this book is an ideal resource for students, researchers and practitioners seeking an understanding of the processes that give rise to volcanic deformation, earthquakes, and eruptions.

This book includes research papers from the 11th National Technical Symposium on Unmanned System Technology. Covering a number of topics, including intelligent robotics, novel sensor technology, control algorithms, acoustics signal processing, imaging techniques, biomimetic robots, green energy sources, and underwater communication backbones and protocols, it will appeal to researchers developing marine technology solutions and policy-makers interested in technologies to facilitate the exploration of coastal and oceanic regions.

Analytical mechanics is a set of mathematical tools used to describe a wide range of physical systems, both in classical mechanics and beyond. It offers a powerful and elegant alternative to Newtonian mechanics; however it can be challenging to learn due to its high degree of mathematical complexity. Designed to offer a more intuitive guide to this abstract topic, this guide explains the mathematical theory underlying analytical mechanics; helping students to formulate, solve and interpret complex problems using these analytical tools. Each chapter begins with an example of a physical system to illustrate the theoretical steps to be developed in that chapter, and ends with a set of exercises to further develop students' understanding. The book presents the fundamentals of the subject in depth before extending the theory to more elaborate systems, and includes a further reading section to ensure that this is an accessible companion to all standard textbooks.

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.

This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) that is needed to succeed in science courses. The focus is on math actually used in physics, chemistry, and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. Detailed illustrations and links to reference material online help further comprehension. The second edition features new problems and illustrations and features expanded chapters on matrix algebra and differential equations. Use of proven pedagogical techniques developed during the author’s 40 years of teaching experience New practice problems and exercises to enhance comprehension Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables