# 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:**5486

* 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:**8062

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 Mechanics

**Author**: V.I. Arnol'd**Publisher:**Springer Science & Business Media**ISBN:**1475720637**Category:**Mathematics**Page:**520**View:**6408

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

## Primer of Quantum Mechanics

**Author**: Marvin Chester**Publisher:**Courier Corporation**ISBN:**0486138208**Category:**Science**Page:**328**View:**1147

Introductory text examines classical quantum bead on a track: state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; bead in spherical shell. 1992 edition.

## Nano- and Micro-Electromechanical Systems

*Fundamentals of Nano- and Microengineering, Second Edition*

**Author**: Sergey Edward Lyshevski**Publisher:**CRC Press**ISBN:**0849328381**Category:**Technology & Engineering**Page:**744**View:**7364

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 Methods of Classical Physics

**Author**: Vicente Cortés,Alexander S. Haupt**Publisher:**Springer**ISBN:**3319564633**Category:**Science**Page:**99**View:**4749

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.

## Many-Body Problems and Quantum Field Theory

*An Introduction*

**Author**: Philippe-André Martin,Francois Rothen**Publisher:**Springer Science & Business Media**ISBN:**3662048949**Category:**Science**Page:**441**View:**470

Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a substantially new treatment of nucleon pairing.

## Modeling and Simulation of Aerospace Vehicle Dynamics

**Author**: Peter H. Zipfel**Publisher:**AIAA**ISBN:**9781563474569**Category:**Science**Page:**551**View:**5066

This book unifies all aspects of flight dynamics for the efficient development of aerospace vehicle simulations. It provides the reader with a complete set of tools to build, program, and execute simulations. Unlike other books, it uses tensors for modeling flight dynamics in a form invariant under coordinate transformations. For implementation, the tensors are converted to matrices, resulting in compact computer code. The reader can pick templates of missiles, aircraft, or hypersonic vehicles to jump-start a particular application. It is the only textbook that combines the theory of modeling with hands-on examples of three-, five-, and six-degree-of-freedom simulations. Included is a link to the CADAC Web Site where you may apply for the free CADAC CD with eight prototype simulations and plotting programs. Amply illustrated with 318 figures and 44 examples, the text can be used for advanced undergraduate and graduate instruction or for self-study. Also included are 77 problems that enhance the ability to model aerospace vehicles and nine projects that hone the skills for developing three-, five-, and six-degree-of-freedom simulations.

## 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:**9453

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.

## Quantum Theory for Mathematicians

**Author**: Brian C. Hall**Publisher:**Springer Science & Business Media**ISBN:**1461471168**Category:**Science**Page:**554**View:**5405

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

## Chaotic Dynamics

*An Introduction Based on Classical Mechanics*

**Author**: Tamás Tél,Márton Gruiz**Publisher:**Cambridge University Press**ISBN:**9780521547833**Category:**Mathematics**Page:**393**View:**9482

A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.

## Fundamental Principles of Classical Mechanics

*A Geometrical Perspective*

**Author**: Kai S Lam**Publisher:**World Scientific Publishing Company**ISBN:**9814551503**Category:**Science**Page:**592**View:**9346

This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

## The Elements of Mechanics

**Author**: Giovanni Gallavotti**Publisher:**Springer Science & Business Media**ISBN:**3662007312**Category:**Science**Page:**575**View:**8203

The word "elements" in the title of this book does not convey the implica tion that its contents are "elementary" in the sense of "easy": it mainly means that no prerequisites are required, with the exception of some basic background in classical physics and calculus. It also signifies "devoted to the foundations". In fact, the arguments chosen are all very classical, and the formal or technical developments of this century are absent, as well as a detailed treatment of such problems as the theory of the planetary motions and other very concrete mechanical problems. This second meaning, however, is the result of the necessity of finishing this work in a reasonable amount of time rather than an a priori choice. Therefore a detailed review of the "few" results of ergodic theory, of the "many" results of statistical mechanics, of the classical theory of fields (elasticity and waves), and of quantum mechanics are also totally absent; they could constitute the subject of two additional volumes on mechanics. This book grew out of several courses on meccanica razionaie, i.e., essentially, theoretical mechanics, which I gave at the University of Rome during the years 1975-1978.

## Solid State and Quantum Theory for Optoelectronics

**Author**: Michael A. Parker**Publisher:**CRC Press**ISBN:**9781420019452**Category:**Science**Page:**848**View:**6193

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.

## 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:**600

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.

## Quantum Field Theory for the Gifted Amateur

**Author**: Tom Lancaster,Stephen J. Blundell,Stephen Blundell**Publisher:**Oxford University Press**ISBN:**0199699321**Category:**Science**Page:**485**View:**5919

Quantum field theory provides the theoretical backbone to most modern physics. This book is designed to bring quantum field theory to a wider audience of physicists. It is packed with worked examples, witty diagrams, and applications intended to introduce a new audience to this revolutionary theory.

## Chern-Simons Theory, Matrix Models, and Topological Strings

**Author**: Marcos Marino**Publisher:**Oxford University Press**ISBN:**9780198568490**Category:**Science**Page:**197**View:**764

After an introduction to matrix models and Cherns-Simons gauge theory, this book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implication of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory.

## Duality System in Applied Mechanics and Optimal Control

**Author**: Wan-Xie Zhong**Publisher:**Springer Science & Business Media**ISBN:**1402078803**Category:**Mathematics**Page:**456**View:**2901

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.

## Kinetic Boltzmann, Vlasov and Related Equations

**Author**: Alexander Sinitsyn,Victor Vedenyapin,Eugene Dulov**Publisher:**Elsevier**ISBN:**0123877792**Category:**Mathematics**Page:**304**View:**679

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions

## The Oxford Companion to Classical Civilization

**Author**: Simon Hornblower,Antony Spawforth,Esther Eidinow**Publisher:**OUP Oxford**ISBN:**0191016764**Category:**History**Page:**912**View:**7142

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.