Geometry and Kinematics

Author: Sawa Manoff

Publisher: Nova Science Pub Incorporated

ISBN: 9781590334362

Category: Science

Page: 527

View: 8586

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.
Read More

Author: Sawa Manoff

Publisher: Nova Science Pub Incorporated

ISBN: 9781590334362

Category: Science

Page: 527

View: 2278

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.
Read More

Application to Mechanics, Gravitation, and Electromagnetism

Author: Lalaonirina R. Rakotomanana

Publisher: Springer

ISBN: 331991782X

Category: Science

Page: 325

View: 3249

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation. It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method. Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.
Read More

Mathematics, Physics and Philosophy

Author: Kobzarev,Y.I. Manin

Publisher: Springer Science & Business Media

ISBN: 940092271X

Category: Science

Page: 214

View: 2599

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.
Read More

Author: Giorgio Ferrarese,Donato Bini

Publisher: Springer

ISBN: 3540731687

Category: Science

Page: 340

View: 5957

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.
Read More

Theory and Related Problems

Author: Petre P. Teodorescu

Publisher: Springer Science & Business Media

ISBN: 9400726163

Category: Science

Page: 802

View: 6930

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.
Read More

A Study of Conservation Principles with Applications

Author: J. N. Reddy

Publisher: Cambridge University Press

ISBN: 1139486152

Category: Technology & Engineering

Page: N.A

View: 3635

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.
Read More

Structure, Examples, Philosophical Problems

Author: W. Balzer,D. Pearce,Heinz-Jürgen Schmidt

Publisher: Springer Science & Business Media

ISBN: 9400964544

Category: Science

Page: 446

View: 2830

The papers in this volume were presented at the colloquium "Reduktion in der Wissenschaft: Struktur, Beispiele, philos ophische PrObleme", held in Bielefeld, West Germany, July 18- 21, 1983. Altogether eighteen talks were delivered at the symposium, and all appear here with the exception of Professor Ehlers' address. In addition, we are pleased to be able to include three papers by invited participants (Kamiah, Ludwig, Scheibe) who were unable to attend the meeting. The meeting itself brought together a sizeable group of logicians, philosophers and working scientists to discuss and debate the theme of reduction, one that occupies a central place in contemporary philosophy of science. The participants and contributors succeeded in opening up new directions in reduction studies and presenting fresh case studies of re duction from many different areas of scientific practice. Their efforts will greatly enhance our understanding of reduction and, consequently, our grasp of the complex process of scien tific change and the unity and growth of scientific knowledge.
Read More

Kinematics and Statics

Author: Jan Awrejcewicz

Publisher: Springer Science & Business Media

ISBN: 1461437911

Category: Science

Page: 440

View: 2305

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.
Read More

Author: Jadran Lenarčič,Bahram Ravani

Publisher: Springer Science & Business Media

ISBN: 940158348X

Category: Technology & Engineering

Page: 514

View: 9184

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.
Read More

Author: Michael Bitbol

Publisher: Springer Science & Business Media

ISBN: 9400917724

Category: History

Page: 292

View: 2941

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.
Read More

Author: Oleg Mikhaĭlovich Belot︠s︡erkovskiĭ,I?U?. I. Khlopkov

Publisher: World Scientific

ISBN: 9814282367

Category: Mathematics

Page: 280

View: 5156

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.
Read More

Author: Simon R. Eugster

Publisher: Springer

ISBN: 3319164953

Category: Technology & Engineering

Page: 146

View: 4096

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.
Read More

Author: Zhengming Wang,Dongyun Yi,Xiaojun Duan,Jing Yao,Defeng Gu

Publisher: CRC Press

ISBN: 1439853789

Category: Mathematics

Page: 553

View: 3766

Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics. Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference: Introduces the basic concepts of measurements and errors Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data Covers Kalman filtering with colored noises and its applications Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors’ research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.
Read More

Author: Durgaiah D. Rama

Publisher: New Age International

ISBN: 9788122413861

Category: Fluid dynamics

Page: 912

View: 8209

This Book Presents A Thorough And Comprehensive Treatment Of Both The Basic As Well As The More Advanced Concepts In Fluid Mechanics. The Entire Range Of Topics Comprising Fluid Mechanics Has Been Systematically Organised And The Various Concepts Are Clearly Explained With The Help Of Several Solved Examples.Apart From The Fundamental Concepts, The Book Also Explains Fluid Dynamics, Flow Measurement, Turbulent And Open Channel Flows And Dimensional And Model Analysis. Boundary Layer Flows And Compressible Fluid Flows Have Been Suitably Highlighted.Turbines, Pumps And Other Hydraulic Systems Including Circuits, Valves, Motors And Ram Have Also Been Explained. The Book Provides 225 Fully Worked Out Examples And More Than 1600 Questions Including Numerical Problems And Objective Questions. The Book Would Serve As An Exhaustive Text For Both Undergraduate And Post- Graduate Students Of Mechanical, Civil And Chemical Engineering. Amie And Competitive Examination Candidates As Well As Practising Engineers Would Also Find This Book Very Useful.
Read More

Author: Graham Nerlich

Publisher: Cambridge University Press

ISBN: 9780521456456

Category: Philosophy

Page: 290

View: 2279

This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument and investigates how different spaces would affect perception differently. Along the way Professor Nerlich criticizes and rejects conventionalism as a non-realist metaphysics of space, concluding that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, while offering an extensive discussion of the relativity of motion.
Read More

Author: Leo Dorst,Chris Doran,Joan Lasenby

Publisher: Springer Science & Business Media

ISBN: 146120089X

Category: Mathematics

Page: 478

View: 2409

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.
Read More

New Interplays : a Volume in Honor of Sergio Albeverio : Proceedings of the Conference on Infinite Dimensional (Stochastic) Analysis and Quantum Physics, Max Planck Institute for Mathematics in the Sciences, Leipzig, January 18-22, 1999

Author: Sergio Albeverio

Publisher: American Mathematical Soc.

ISBN: 9780821819609

Category: Mathematics

Page: 333

View: 4245

This volume and ""Stochastic Processes, Physics and Geometry: New Interplays I"" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, 'Infinite Dimensional (Stochastic) Analysis and Quantum Physics', was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and non commutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.
Read More

The Structuralist Program

Author: W. Balzer,C.U. Moulines,J.D. Sneed

Publisher: Springer Science & Business Media

ISBN: 9400937652

Category: Science

Page: 440

View: 2283

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness.
Read More