Author: Sawa Manoff

Publisher: Nova Science Pub Incorporated

ISBN: 9781590334362

Category: Science

Page: 527

View: 4849

The main idea of this book is, on the grounds of the differential-geometric structures of the (Ln, g)-spaces and the kinematics of vector fields to set the stage for the study of physical and gravitational physical interactions. In order to accomplish this task, the book is divided into three parts. Part One briefly reviews and introduces the problems of theoretical gravitational physics. Part Two deals with the theory of differentiable manifolds with contravariant affine connections and metrics. Part Three investigates the kinematics of vector fields over (Ln, g)-spaces.
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Geometry and Kinematics

Author: Sawa Manoff

Publisher: Nova Science Pub Incorporated

ISBN: 9781590334362

Category: Science

Page: 527

View: 5574

The main idea of this book is, on the grounds of the differential-geometric structures of the (Ln, g)-spaces and the kinematics of vector fields to set the stage for the study of physical and gravitational physical interactions. In order to accomplish this task, the book is divided into three parts. Part One briefly reviews and introduces the problems of theoretical gravitational physics. Part Two deals with the theory of differentiable manifolds with contravariant affine connections and metrics. Part Three investigates the kinematics of vector fields over (Ln, g)-spaces.
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Author: John D Clayton

Publisher: World Scientific

ISBN: 9814616052

Category: Mathematics

Page: 192

View: 9939

This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided. Contents: IntroductionGeometric FundamentalsKinematics of Integrable DeformationGeometry of Anholonomic DeformationKinematics of Anholonomic DeformationList of SymbolsBibliographyIndex Readership: Researchers in mathematical physics and engineering mechanics. Key Features:Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new resultsLine-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final resultsGeneral analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectivelyKeywords:Differential Geometry;Tensor Analysis;Continuum Mechanics;Kinematics;Deformation;Anholonomic Coordinates
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Mathematics, Physics and Philosophy

Author: Kobzarev,Y.I. Manin

Publisher: Springer Science & Business Media

ISBN: 940092271X

Category: Science

Page: 214

View: 7378

This book has come into being as a result of scientific debates. And these debates have determined its structure. The first chapter is in the form of Socratic dialogues between a mathematician (MATH.), two physicists (pHYS. and EXP.) and a philosopher (PHIL.). However, although one of the authors is a theoretical physicist and the other a mathematician, the reader must not think that their opinions have been divided among the participants of the dialogues. We have tried to convey the inner tension of the topic under discussion and its openness. The attitudes of the participants reflect more the possible evaluations of the situation rather than the actual views of the authors. What is more, the subject "elementary particles" as dealt with in the 3 6 dialogue stretches over (2-3) 10 years of historical time and a space of 10 ±1 pages of scientific literature. For this reason, a complete survey of it is un achievable. But, of course, every researcher constructs his own history of his science and sees a certain list of its main pOints. We have attempted to float several possible pictures of this kind. Therefore the fact that Math and Phys talk about the history of element ary particles is not an attempt to present the scientific history of this realm of physics.
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A Study of Conservation Principles with Applications

Author: J. N. Reddy

Publisher: Cambridge University Press

ISBN: 1139486152

Category: Technology & Engineering

Page: N.A

View: 4523

As most modern technologies are no longer discipline-specific but involve multidisciplinary approaches, undergraduate engineering students should be introduced to the principles of mechanics so that they have a strong background in the basic principles common to all disciplines and are able to work at the interface of science and engineering disciplines. This textbook is designed for a first course on principles of mechanics and provides an introduction to the basic concepts of stress and strain and conservation principles. It prepares engineer-scientists for advanced courses in traditional as well as emerging fields such as biotechnology, nanotechnology, energy systems, and computational mechanics. This simple book presents the subjects of mechanics of materials, fluid mechanics, and heat transfer in a unified form using the conservation principles of mechanics.
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Theory and Related Problems

Author: Petre P. Teodorescu

Publisher: Springer Science & Business Media

ISBN: 9400726163

Category: Science

Page: 802

View: 5228

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.
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A Case Study in Kinematics

Author: Glenn A. Kramer

Publisher: MIT Press

ISBN: 9780262111645

Category: Computers

Page: 277

View: 9560

Solving Geometric Constraints records and explains the formal basis for graphical analysis techniques that have been used for decades in engineering disciplines. It describes a novel computer implementation of a 3D graphical analysis method - degrees of freedom analysis - for solving geometric constraint problems of the type encountered in the kinematic analysis of mechanical linkages, providing the best computational bounds yet achieved for this class of problems. The technique allows for the design of algorithms that provide significant speed increases and. will foster the development of interactive software tools for the simulation, optimization, and design of complex mechanical devices as well as provide leverage in other geometric domains. Kramer formalizes symbolic geometry, including explicit reasoning about degrees of freedom, as an alternative to symbolic algebraic or iterative numerical techniques for solving geometric constraint satisfaction problems. He discusses both the theoretical and practical advantages of degrees of freedom analysis, including a correctness proof of the procedure, and clearly defines its scope. He covers all nondegenerate cases and handles several classes of degeneracy, giving examples that are practical and of representative complexity.
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Structure, Examples, Philosophical Problems

Author: Wolfgang Balzer,D. Pearce,Heinz-Juergen Schmidt

Publisher: Springer Science & Business Media

ISBN: 9400964544

Category: Science

Page: 446

View: 2712

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From Initial Inversion to Full Accretion

Author: M. Nemčok,A. Mora,J.W. Cosgrove

Publisher: Geological Society of London

ISBN: 1862393583

Category: Science

Page: 482

View: 6974

This volume studies the driving dynamic for thick-skin tectonics. It evaluates the role of various factors that control the development of thick-skin architecture. The studied driving dynamics include individual plate movement rates, overall convergence rates, orogen movement sense with respect to mantle flow and pro-wedge versus retro-wedge location. Numerous internal factors that influence the architecture of thick-skinned dominated orogens have been considered. These include the role of the rheology of the deforming layers, the presence or absence of potential detachment horizons, basement buttresses, crustal thickness variations, inherited strength contrasts and the impact of pre-existing anisotropy in thick-skin orogenic deformation. External factors discussed include the role of both syn-tectonic erosion and deposition in deformation. The study areas begin with worldwide examples and close with a detailed coverage of the Northern Andes natural laboratory, which is characterized by particularly robust data coverage.
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Author: Simon Eugster

Publisher: Springer

ISBN: 3319164953

Category: Technology & Engineering

Page: 146

View: 3720

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
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Author: Giorgio Ferrarese,Donato Bini

Publisher: Springer

ISBN: 3540731687

Category: Science

Page: 340

View: 7918

This mathematically-oriented introduction takes the point of view that students should become familiar, at an early stage, with the physics of relativistic continua and thermodynamics within the framework of special relativity. Therefore, in addition to standard textbook topics such as relativistic kinematics and vacuum electrodynamics, the reader will be thoroughly introduced to relativistic continuum and fluid mechanics. There is emphasis on the 3+1 splitting technique.
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Author: A. L. Stanford,J. M. Tanner

Publisher: Academic Press

ISBN: 148322029X

Category: Science

Page: 816

View: 561

Physics for Students of Science and Engineering is a calculus-based textbook of introductory physics. The book reviews standards and nomenclature such as units, vectors, and particle kinetics including rectilinear motion, motion in a plane, relative motion. The text also explains particle dynamics, Newton's three laws, weight, mass, and the application of Newton's laws. The text reviews the principle of conservation of energy, the conservative forces (momentum), the nonconservative forces (friction), and the fundamental quantities of momentum (mass and velocity). The book examines changes in momentum known as impulse, as well as the laws in momentum conservation in relation to explosions, collisions, or other interactions within systems involving more than one particle. The book considers the mechanics of fluids, particularly fluid statics, fluid dynamics, the characteristics of fluid flow, and applications of fluid mechanics. The text also reviews the wave-particle duality, the uncertainty principle, the probabilistic interpretation of microscopic particles (such as electrons), and quantum theory. The book is an ideal source of reference for students and professors of physics, calculus, or related courses in science or engineering.
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Author: Leo Dorst,Chris Doran,Joan Lasenby

Publisher: Springer Science & Business Media

ISBN: 146120089X

Category: Mathematics

Page: 478

View: 2128

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
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Proceedings of a Symposium

Author: Commission on Physical Sciences, Mathematics, and Applications,Board on Mathematical Sciences,Division on Engineering and Physical Sciences,National Research Council

Publisher: National Academies Press

ISBN: 030905785X

Category: Mathematics

Page: 80

View: 8549

Some of the modem developments described in Motion, Control, and Geometry include the geometric control of robot motion and craft orientation, how high-power precision micromotors are engineered for less invasive surgery and self-focusing lens applications, what a mobile robot on a surface has in common with one moving in three dimensions, and how the motion-control problem is simplified by a coupled oscillator's geometric grouping of degrees of freedom and motion time scales. The four papers in these proceedings provide a view through the scientific portal of today's motion-control geometric research into tomorrow's technology. The mathematics needed to carry out this research is that of modem differential geometry, and the questions raised in the field of motion-control geometry go directly to the research frontier. Geometry is a mathematical area too often neglected nowadays in a student's education. This publication will help adjust the control initially imposed about 2,300 years ago on one kind of "motion"- that of students entering Plato's Academy, where the following caveat was inscribed above the doorway: "Let no one ignorant of geometry enter here." Readers of these chapters will gain an appreciation of modem geometry and how it continues to play a crucial role in the context of motion control in cutting-edge science and technology.
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Kinematics and Statics

Author: Jan Awrejcewicz

Publisher: Springer Science & Business Media

ISBN: 1461437911

Category: Science

Page: 440

View: 7527

This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.
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Author: Jadran Lenarčič,Bahram Ravani

Publisher: Springer Science & Business Media

ISBN: 940158348X

Category: Technology & Engineering

Page: 514

View: 3225

Recently, research in robot kinematics has attracted researchers with different theoretical profiles and backgrounds, such as mechanical and electrica! engineering, computer science, and mathematics. It includes topics and problems that are typical for this area and cannot easily be met elsewhere. As a result, a specialised scientific community has developed concentrating its interest in a broad class of problems in this area and representing a conglomeration of disciplines including mechanics, theory of systems, algebra, and others. Usually, kinematics is referred to as the branch of mechanics which treats motion of a body without regard to the forces and moments that cause it. In robotics, kinematics studies the motion of robots for programming, control and design purposes. It deals with the spatial positions, orientations, velocities and accelerations of the robotic mechanisms and objects to be manipulated in a robot workspace. The objective is to find the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and to discover and visualise analytical tools for understanding and evaluation of motion properties ofvarious mechanisms used in a robotic system.
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Author: Michel Bitbol

Publisher: Springer Science & Business Media

ISBN: 9400917724

Category: History

Page: 292

View: 3545

This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950's for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger's published papers and books of the same period. However, they were likely to be misinterpreted out of their context. The problem was that current scholarship could not help very much the reader of these writings to figure out their significance. The few available studies about SchrOdinger's interpretation of quantum mechanics are generally excellent, but almost entirely restricted to the initial period 1925-1927. Very little work has been done on Schrodinger's late views on the theory he contributed to create and develop. The generally accepted view is that he never really recovered from his interpretative failure of 1926-1927, and that his late reflections (during the 1950's) are little more than an expression of his rising nostalgia for the lost ideal of picturing the world, not to say for some favourite traditional picture. But the content and style of Schrodinger's texts of the 1950's do not agree at all with this melancholic appraisal; they rather set the stage for a thorough renewal of accepted representations. In order to elucidate this paradox, I adopted several strategies.
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Author: Oleg Mikhaĭlovich Belot︠s︡erkovskiĭ,I?U?. I. Khlopkov

Publisher: World Scientific

ISBN: 9814282367

Category: Mathematics

Page: 280

View: 6294

This book is devoted to analysis of Monte Carlo methods developed in rarefied gas dynamics. Presented is the short history of the development of such methods, described are their main properties, their advantages and deficiencies. It is shown that the contemporary stage in the progress of computational methods cannot be regarded without a complex approach to the preparation of algorithms taking into account all the peculiarities of the problem under consideration, that is, of the physical nature of a process, the mathematical model and the theoretical aspects of computational mathematics and stochastic processes. Thoroughly investigated is the possibility of application of Monte Carlo methods in some kindred areas of science which are non-traditional for the use of statistical modeling (continuous media, turbulence). Considered are the possible directions of development of statistical modeling.
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Author: Vesselin Petkov

Publisher: Springer Science & Business Media

ISBN: 3642019625

Category: Science

Page: 316

View: 6217

Puts the emphasis on conceptual questions: Why is there no such thing as absolute motion? What is the physical meaning of relativity of simultaneity? But, the most important question that is addressed in this book is "what is the nature of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?" Develops answers to these questions via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional. Discusses the implication of the result (this analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible) for physics, philosophy, and our entire world view are discussed.
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Space and Time

Author: Tim Maudlin

Publisher: Princeton University Press

ISBN: 0691143099

Category: Philosophy

Page: 183

View: 9739

Introduces non-physicists to core philosophical issues surrounding the nature & structure of space & time, & is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Provides a broad historical overview, from Aristotle to Einstein, & covers the Twins Paradox, Galilean relativity, time travel, & more.
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