# Search Results for "classical-mechanics-theory-and-mathematical-modeling-cornerstones"

## Classical Mechanics

*Theory and Mathematical Modeling*

**Author**: Emmanuele DiBenedetto**Publisher:**Springer Science & Business Media**ISBN:**9780817646486**Category:**Mathematics**Page:**351**View:**7429

* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

## Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

**Author**: Michal Fečkan,Michal Pospíšil**Publisher:**Academic Press**ISBN:**0128043644**Category:**Mathematics**Page:**260**View:**524

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them Investigates the relationship between non-smooth systems and their continuous approximations

## Mathematical Methods of Classical Physics

**Author**: Vicente Cortés,Alexander S. Haupt**Publisher:**Springer**ISBN:**3319564633**Category:**Science**Page:**99**View:**5773

This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.

## Nano- and Micro-Electromechanical Systems

*Fundamentals of Nano- and Microengineering, Second Edition*

**Author**: Sergey Edward Lyshevski**Publisher:**CRC Press**ISBN:**1351835173**Category:**Technology & Engineering**Page:**744**View:**7278

Society is approaching and advancing nano- and microtechnology from various angles of science and engineering. The need for further fundamental, applied, and experimental research is matched by the demand for quality references that capture the multidisciplinary and multifaceted nature of the science. Presenting cutting-edge information that is applicable to many fields, Nano- and Micro-Electromechanical Systems: Fundamentals of Nano and Microengineering, Second Edition builds the theoretical foundation for understanding, modeling, controlling, simulating, and designing nano- and microsystems. The book focuses on the fundamentals of nano- and microengineering and nano- and microtechnology. It emphasizes the multidisciplinary principles of NEMS and MEMS and practical applications of the basic theory in engineering practice and technology development. Significantly revised to reflect both fundamental and technological aspects, this second edition introduces the concepts, methods, techniques, and technologies needed to solve a wide variety of problems related to high-performance nano- and microsystems. The book is written in a textbook style and now includes homework problems, examples, and reference lists in every chapter, as well as a separate solutions manual. It is designed to satisfy the growing demands of undergraduate and graduate students, researchers, and professionals in the fields of nano- and microengineering, and to enable them to contribute to the nanotechnology revolution.

## Mathematical Modeling for Complex Fluids and Flows

**Author**: Michel Deville,Thomas B. Gatski**Publisher:**Springer Science & Business Media**ISBN:**364225294X**Category:**Mathematics**Page:**264**View:**5274

Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects. Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.

## Essentials of Hamiltonian Dynamics

**Author**: John H. Lowenstein**Publisher:**Cambridge University Press**ISBN:**1139504738**Category:**Science**Page:**N.A**View:**923

Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica® are available online at www.cambridge.org/Lowenstein.

## Solid State and Quantum Theory for Optoelectronics

**Author**: Michael A. Parker**Publisher:**CRC Press**ISBN:**9781420019452**Category:**Science**Page:**848**View:**9182

While applications rapidly change one to the next in our commercialized world, fundamental principles behind those applications remain constant. So if one understands those principles well enough and has ample experience in applying them, he or she will be able to develop a capacity for reaching results via conceptual thinking rather than having to always rely on models to test various conditions. In Solid State and Quantum Theory for Optoelectronics, Michael Parker provides a general conceptual framework for matter that leads to the matter-light interaction explored in the author’s Physics of Optoelectronics (CRC Press). Instead of overburdening readers with the definition–theorem– proof format often expected in mathematics texts, this book instructs readers through the development of conceptual pictures. Employing a proven pedagogic approach, as rigorous as it is intuitive, Professor Parker – Provides several lead-ins to the quantum theory including a brief review of Lagrange and Hamilton’s approach to classical mechanics and the fundamental quantum link with Hilbert space Demonstrates the Schrödinger wave equation from the Feynman path integral Discusses standard topics such as the quantum well, harmonic oscillator, representations, perturbation theory, and spin Expands discussion from the density operator and its applications to quantum computing and teleportation Provides the concepts for ensembles and microstates in detail with emphasis on the derivation of particle population distributions across energy levels Professors Parker includes problems to help readers understand and internalize the material. But just as important, the working-through of these problems will help readers develop the sort of approach that, instead of wholly relying on models, enables them to extrapolate solutions guided by informed intuition developed over the course of formal study and laboratory experiment. It is the kind of conceptual thinking that will allow readers to move with deeper understanding from optical applications to more theoretical topics in physics.

## Duality System in Applied Mechanics and Optimal Control

**Author**: Wan-Xie Zhong**Publisher:**Springer Science & Business Media**ISBN:**1402078803**Category:**Mathematics**Page:**456**View:**6473

A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: -Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems. -Canonical transformation applied to non-linear systems. -Pseudo-excitation method for structural random vibrations. -Precise integration of two-point boundary value problems. -Wave propagation along wave-guides, scattering. -Precise solution of Riccati differential equations. -Kalman filtering. -HINFINITY theory of control and filter.

## The Oxford Companion to Classical Civilization

**Author**: Simon Hornblower,Antony Spawforth,Esther Eidinow**Publisher:**OUP Oxford**ISBN:**0191016764**Category:**History**Page:**912**View:**6457

What did the ancient Greeks eat and drink? What role did migration play? Why was emperor Nero popular with the ordinary people but less so with the upper classes? Why (according to ancient authors) was Oedipus ('with swollen foot') so called? For over 2,000 years the civilizations of ancient Greece and Rome have captivated our collective imagination and provided inspiration for so many aspects of our lives, from culture, literature, drama, cinema, and television to society, education, and politics. Many of the roots of the way life is lived in the West today can be traced to the ancient civilizations, not only in politics, law, technology, philosophy, and science, but also in social and family life, language, and art. Beautiful illustrations, clear and authoritative entries, and a useful chronology and bibliography make this Companion the perfect guide for readers interested in learning more about the Graeco-Roman world. As well as providing sound information on all aspects of classical civilization such as history, politics, ethics, morals, law, society, religion, mythology, science and technology, language, literature, art, and scholarship, the entries in the Companion reflect the changing interdisciplinary aspects of classical studies, covering broad thematic subjects, such as race, nationalism, gender, ethics, and ecology, confirming the impact classical civilizations have had on the modern world.

## Developments in Mathematical and Experimental Physics

*Volume A: Cosmology and Gravitation*

**Author**: Alfredo Macias,Francisco Uribe,Enrique Diaz**Publisher:**Springer Science & Business Media**ISBN:**9780306472930**Category:**Science**Page:**300**View:**6324

The first part is devoted to the topic of quantum gravity and string theories, mainly concerned with recent authoritative results in the study of discretizations in classical and quantum general relativity, non-commutative theories of gravity, (2+1)-dimensional supergravity, and Berezin description of Kaehler quotients. The field to particle transition problem is also considered. The second part deals with cosmology and black holes. Here, cosmological, inflationary, and braneworld scenarios are investigated. Moreover, some scalar field models for the dark matter content of the universe as well as new models of protostellar collapse and fragmentation are presented. This part includes also a study of de Sitter/Anti-de Sitter phase transition for black holes, an understanding of hairy black holes and an improvement of the no-hair theorem proof for the Proca field. The third part is devoted to exact solutions, in particular classical and quantum cosmological solutions in scalar-tensor theories. Additionally, a discussion about conformally flat axisymmetric spacetimes and some considerations on accelerated expansion in scalar-tensor theories are presented. Experimental and some mixed topics are included in the final part. Among them is an experimental foundation of nonlocality and superluminal signal velocity in photonic tunneling, a proposal for testing the weak equivalence principle for charged particles in space. Moreover, a possible new type of skewon field linked to Maxwell theory is also presented, and an authoritative discussion at the interface of quantum and gravitational realms.

## Linear Algebra with Applications

**Author**: Gareth Williams**Publisher:**Jones & Bartlett Learning**ISBN:**9780763732356**Category:**Mathematics**Page:**670**View:**3459

Mathematics

## Classical and Modern Diffraction Theory

**Author**: Kamill Klem-Musatov,Henning C. Hoeber,Tijmen Jan Moser,Michael A. Pelissier**Publisher:**SEG Books**ISBN:**1560803223**Category:**Science**Page:**352**View:**9039

Providing geophysicists with an in-depth understanding of the theoretical and applied background for the seismic diffraction method, “Classical and Modern Diffraction Theory” covers the history and foundations of the classical theory and the key elements of the modern diffraction theory. Chapters include an overview and a historical review of classical theory, a summary of the experimental results illustrating this theory, and key principles of the modern theory of diffraction; the early cornerstones of classical diffraction theory, starting from its inception in the 17th century and an extensive introduction to reprinted works of Grimaldi, Huygens, and Young; details of the classical theory of diffractions as developed in the 19th century and reprinted works of Fresnel, Green, Helmholtz, Kirchhoff, and Rayleigh; and the cornerstones of the modern theory including Keller’s geometrical theory of diffraction, boundary-layer theory, and super-resolution. Appendices on the Cornu spiral and Babinet’s principle are also included.

## Relativity

*The Special and the General Theory*

**Author**: Albert Einstein,Robert W. Lawson,Amit Hagar**Publisher:**Barnes & Noble Publishing**ISBN:**9780760759219**Category:**Science**Page:**125**View:**2927

Albert Einstein's Relativity: The Special and the General Theory (1920) is a cornerstone of modern physics. Einstein intended this book for "those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus." Indeed, within the vast literature on the philosophy of space and time, Einstein's Relativity shall remain an illuminable and intelligible exposition, highly quotable as one of the most lucid presentations of the subject matter, and a launching pad for any further inquiry on the fascinating features of our universe.

## SCi Simulation

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Computer simulation**Page:**N.A**View:**8301

## Lectures on algebraic quantum field theory and operator algebras

**Author**: Bert Schroer,Centro Brasileiro de Pesquisas Físicas**Publisher:**N.A**ISBN:**N.A**Category:**Science**Page:**71**View:**4253

## Approaching Quantum Computing

**Author**: Dan C. Marinescu,Gabriela M. Marinescu**Publisher:**Prentice Hall**ISBN:**9780131452244**Category:**Computers**Page:**386**View:**2455

With a clear writing style and matter-of-fact approach, this rigorous yet accessible introduction to quantum computing is designed for readers with a solid mathematical background but limited knowledge of physics and quantum mechanics. Using a methodical approach and an abundance of worked examples, this handbook delivers a thorough introduction to the quantum circuit model, including the mathematical formalism required for quantum computing. Concentrates on the quantum circuit model to make complex subject matter more accessible. Provides a phenomenological introduction to quantum computing, encouraging readers to view the subject as a fundamentally new approach to computing. Detailed presentation of quantum algorithms demonstrates the logic behind the development of Deutsch's problem, quantum Fourier transform, Shor's factoring algorithm, Simon's algorithm for phase estimation, and discrete logarithms evaluation problems. For anyone interested in learning more about quantum computing.

## Intermittency in Turbulent Flows

**Author**: J. C. Vassilicos,Department of Applied Mathematics and Theoretical Physics J C Vassilicos**Publisher:**Cambridge University Press**ISBN:**9780521792219**Category:**Mathematics**Page:**276**View:**2652

Turbulence, intermittency, nonlinear dynamics, fluid mechanics.

## Essays on the Future

*In Honor of Nick Metropolis*

**Author**: Siegfried Hecker,Gian-Carlo Rota**Publisher:**Springer Science & Business Media**ISBN:**9780817638566**Category:**Science**Page:**276**View:**2252

This collection represents a unique undertaking in scientific publishing to honor Nick Metropolis, the last survivor of the World War II Manhattan Project in Los Alamos. In this volume, some of the leading scientists and humanists of our time have contributed essays related to their respective disciplines, exploring various aspects of future developments in science and society, philosophy, national security, nuclear power, pure and applied mathematics, physics and biology, particle physics, computing, and information science.

## Chemistry and Society

**Author**: Leo Schubert,Luis A. Veguilla-Berdecia**Publisher:**N.A**ISBN:**N.A**Category:**Bioquimica**Page:**341**View:**2665

## Principles of Quantum General Relativity

**Author**: Eduard Prugove?ki**Publisher:**World Scientific**ISBN:**9789810221386**Category:**Science**Page:**351**View:**9795

This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.