Download or read book Variational Methods in Theoretical Mechanics written by J.T. Oden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .
Download or read book Continuum Mechanics and Theory of Materials written by Peter Haupt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Theoretical Mechanics written by Brian H. Chirgwin and published by Elsevier. This book was released on 2013-10-22 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Theoretical Mechanics deals with advanced theoretical mechanics in three dimensions, making use of concepts and methods such as matrices, vectors, tensors, and transformation methods. The definition of a vector via the transformation law obeyed by its components is emphasized, and matrix methods are used to handle sets of components. Special attention is given to the definition of angular velocity and the proof that it can be represented by a vector. This book is comprised of 11 chapters and begins with an introduction to kinematics in three dimensions. Lagrange's equations and analytical dynamics are then presented, along with the simpler problems of three-dimensional dynamics, often with the help of rotating axes. Stability and small oscillations are also considered. The subsequent chapters focus on the dynamics of a particle and the motion of a system of particles; gyroscopic motion, free rotation, and steady motion; oscillations of a dynamical system with a finite number of degrees of freedom; and the vibrations of strings. The final chapter is devoted to analytical dynamics, paying particular attention to Hamilton's principle and equations of motion as well as the Hamilton-Jacobi equation. This monograph is intended for engineers and scientists as well as students of mathematics, physics, and engineering.
Download or read book Classical Mechanics with Mathematica written by Antonio Romano and published by Springer. This book was released on 2018-05-29 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments. The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material. Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
Download or read book A Student s Guide to Lagrangians and Hamiltonians written by Patrick Hamill and published by Cambridge University Press. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Download or read book Introduction to Unified Mechanics Theory with Applications written by Cemal Basaran and published by Springer Nature. This book was released on 2021-02-02 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the mathematical formulation and proof of the unified mechanics theory (UMT) which is based on the unification of Newton’s laws and the laws of thermodynamics. It also presents formulations and experimental verifications of the theory for thermal, mechanical, electrical, corrosion, chemical and fatigue loads, and it discusses why the original universal laws of motion proposed by Isaac Newton in 1687 are incomplete. The author provides concrete examples, such as how Newton’s second law, F = ma, gives the initial acceleration of a soccer ball kicked by a player, but does not tell us how and when the ball would come to a stop. Over the course of Introduction to Unified Mechanics Theory, Dr. Basaran illustrates that Newtonian mechanics does not account for the thermodynamic changes happening in a system over its usable lifetime. And in this context, this book explains how to design a system to perform its intended functions safely over its usable life time and predicts the expected lifetime of the system without using empirical models, a process currently done using Newtonian mechanics and empirical degradation/failure/fatigue models which are curve-fit to test data. Written as a textbook suitable for upper-level undergraduate mechanics courses, as well as first year graduate level courses, this book is the result of over 25 years of scientific activity with the contribution of dozens of scientists from around the world including USA, Russia, Ukraine, Belarus, Spain, China, India and U.K.
Download or read book Nonlinear Mechanics written by Alexander L. Fetter and published by Courier Corporation. This book was released on 2012-05-04 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their prior Dover book, the authors provided a self-contained account of classical mechanics; this supplement/update offers a bridge to contemporary mechanics. Topics include nonlinear continuous systems. 2006 edition.
Download or read book Principles of Mechanics written by Salma Alrasheed and published by Springer. This book was released on 2019-04-30 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals fully, paving the way to deal with more advanced topics. After solving all of the examples, the reader will have gained a solid foundation in mechanics and the skills to apply the concepts in a variety of situations. The book is useful for undergraduate students majoring in physics and other science and engineering disciplines. It can also be used as a reference for more advanced levels.
Download or read book Analytical Mechanics written by A.I. Lurie and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 859 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a translation of A.I. Lurie’s classical Russian textbook on analytical mechanics. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the 20th century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems.
Download or read book Structure and Interpretation of Classical Mechanics second edition written by Gerald Jay Sussman and published by MIT Press. This book was released on 2015-02-06 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
Download or read book Introduction to Theoretical Mechanics written by Robert A. Becker and published by . This book was released on 2003-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical Mechanics written by John R. Taylor and published by . This book was released on 2004-09-15 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ClassicalMechanics is intended for students who have studied some mechanics in anintroductory physics course.With unusual clarity, the book covers most of the topics normally found in books at this level.
Download or read book Lagrangian And Hamiltonian Mechanics Solutions To The Exercises written by Melvin G Calkin and published by World Scientific Publishing Company. This book was released on 1999-03-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.
Download or read book Classical Mechanics written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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
Download or read book A History of Mechanics written by René Dugas and published by Courier Corporation. This book was released on 2012-11-07 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A remarkable work which will remain a document of the first rank for the historian of mechanics." — Louis de Broglie In this masterful synthesis and summation of the science of mechanics, Rene Dugas, a leading scholar and educator at the famed Ecole Polytechnique in Paris, deals with the evolution of the principles of general mechanics chronologically from their earliest roots in antiquity through the Middle Ages to the revolutionary developments in relativistic mechanics, wave and quantum mechanics of the early 20th century. The present volume is divided into five parts: The first treats of the pioneers in the study of mechanics, from its beginnings up to and including the sixteenth century; the second section discusses the formation of classical mechanics, including the tremendously creative and influential work of Galileo, Huygens and Newton. The third part is devoted to the eighteenth century, in which the organization of mechanics finds its climax in the achievements of Euler, d'Alembert and Lagrange. The fourth part is devoted to classical mechanics after Lagrange. In Part Five, the author undertakes the relativistic revolutions in quantum and wave mechanics. Writing with great clarity and sweep of vision, M. Dugas follows closely the ideas of the great innovators and the texts of their writings. The result is an exceptionally accurate and objective account, especially thorough in its accounts of mechanics in antiquity and the Middle Ages, and the important contributions of Jordanus of Nemore, Jean Buridan, Albert of Saxony, Nicole Oresme, Leonardo da Vinci, and many other key figures. Erudite, comprehensive, replete with penetrating insights, AHistory of Mechanics is an unusually skillful and wide-ranging study that belongs in the library of anyone interested in the history of science.
Download or read book Soft Solids written by Alan D. Freed and published by Birkhäuser. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the physical principles pertinent to the mathematical modeling of soft materials used in engineering practice, including both man-made materials and biological tissues. It is intended for seniors and masters-level graduate students in engineering, physics or applied mathematics. It will also be a valuable resource for researchers working in mechanics, biomechanics and other fields where the mechanical response of soft solids is relevant. Soft Solids: A Primer to the Theoretical Mechanics of Materials is divided into two parts. Part I introduces the basic concepts needed to give both Eulerian and Lagrangian descriptions of the mechanical response of soft solids. Part II presents two distinct theories of elasticity and their associated theories of viscoelasticity. Seven boundary-value problems are studied over the course of the book, each pertaining to an experiment used to characterize materials. These problems are discussed at the end of each chapter, giving students the opportunity to apply what they learned in the current chapter and to build upon the material in prior chapters.
