Download or read book Hamilton s Principle in Continuum Mechanics written by Anthony Bedford and published by Springer Nature. This book was released on 2021-12-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Download or read book Hamilton s principle in continuum mechanics written by A. Bedford and published by . This book was released on 2006 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Principles of Continuum Mechanics written by Victor Berdichevsky and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.
Download or read book Hamiltons Principle in Continuum Mechanics written by Anthony M. Bedford and published by Halsted Press. This book was released on 1986-07-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solved Problems in Lagrangian and Hamiltonian Mechanics written by Claude Gignoux and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
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 An Introduction to Continuum Mechanics written by J. N. Reddy and published by Cambridge University Press. This book was released on 2013-07-29 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.
Download or read book Variational Principles in Classical Mechanics written by Douglas Cline and published by . This book was released on 2018-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.
Download or read book The Lazy Universe written by Jennifer Coopersmith and published by Oxford University Press. This book was released on 2017-04-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.
Download or read book Advanced Engineering Dynamics written by H. Harrison and published by Butterworth-Heinemann. This book was released on 1997-08-01 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Advanced Engineering Dynamics' bridges the gap between elementary dynamics and advanced specialist applications in engineering.It begins with a reappraisal of Newtonian principles before expanding into analytical dynamics typified by the methods of Lagrange and by Hamilton's Principle and rigid body dynamics. Four distinct vehicle types (satellites, rockets, aircraft and cars) are examined highlighting different aspects of dynamics in each case. Emphasis is placed on impact and one dimensional wave propagation before extending the study into three dimensions. Robotics is then looked at in detail, forging a link between conventional dynamics and the highly specialised and distinctive approach used in robotics. The text finishes with an excursion into the Special Theory of Relativity mainly to define the boundaries of Newtonian Dynamics but also to re-appraise the fundamental definitions. Through its examination of specialist applications highlighting the many different aspects of dynamics this text provides an excellent insight into advanced systems without restricting itself to a particular discipline. The result is essential reading for all those requiring a general understanding of the more advanced aspects of engineering dynamics.
Download or read book Continuum Mechanics and Thermodynamics written by Ellad B. Tadmor and published by Cambridge University Press. This book was released on 2012 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.
Download or read book Fundamentals of Continuum Mechanics written by John W. Rudnicki and published by John Wiley & Sons. This book was released on 2014-09-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering
Download or read book Principles of Continuum Mechanics written by Zdeněk Martinec and published by Springer. This book was released on 2019-05-31 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles. In turn, the linear-elastic solids, the ideal liquid and the Newtonian liquid are presented in detail as concrete applications. The book concludes by covering the theory of small motions in a medium with a finite prestress. In general, the emphasis is on presenting the content in a clear and straightforward way that requires only an elementary grasp of calculus, linear algebra, and Newtonian mechanics. The book is intended for students of physics, mechanics, engineering and the geosciences, as well as applied mathematics, with a year or more of college calculus behind them.
Download or read book Classical Mechanics Lecture Notes written by Helmut Haberzettl and published by World Scientific. This book was released on 2021-06-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides lecture materials of a comprehensive course in Classical Mechanics developed by the author over many years with input from students and colleagues alike. The richly illustrated book covers all major aspects of mechanics starting from the traditional Newtonian perspective, over Lagrangian mechanics, variational principles and Hamiltonian mechanics, rigid-body, and continuum mechanics, all the way to deterministic chaos and point-particle mechanics in special relativity. Derivation steps are worked out in detail, illustrated by examples, with ample explanations.Developed by a classroom practitioner, the book provides a comprehensive overview of classical mechanics with judicious material selections that can be covered in a one-semester course thus streamlining the instructor's task of choosing materials for their course. The usefulness for instructors notwithstanding, the primary aim of the book is to help students in their understanding, with detailed derivations and explanations, and provide focused guidance for their studies by repeatedly emphasizing how various topics are tied together by common physics principles.
Download or read book Continuum Mechanics written by A. J. M. Spencer and published by Courier Corporation. This book was released on 2012-06-08 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduate text offers an analysis of deformation and stress, covers laws of conservation of mass, momentum, and energy, and surveys the formulation of mechanical constitutive equations. 1992 edition.
Download or read book Mathematical Theory of Continuum Mechanics written by Rabindranath Chatterjee and published by Alpha Science Int'l Ltd.. This book was released on 1999 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an introduction to the theory of continuum mechanics in a logically satisfying form. A simple knowledge of Cartesian tensors is a sufficient prerequisite for this book. The book deals with two major branches of continuum mechanics - the mechanics of elastic solids and the mechanics of fluids providing the basis of civil and mechanical engineering, applied mathematics and physics. Traditional courses in solid mechanics and fluid mechanics are usually taught separately with emphasis on physical behaviour at the cost of rigorous mathematical foundation neglecting the analogies between solids and fluids. The book brings two disciplines under one roof seeking to generalize and unify specialized topics.
Download or read book Continuum Mechanics Via Problems and Exercises written by Margarita E Eglit and published by World Scientific Publishing Company. This book was released on 1996-10-28 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to help graduate-level students of Continuum Mechanics become more proficient in its applications through the solution of analytical problems. Published as two separate books — Part I on Theory and Problems with Part II providing Solutions to the problems — professors may also find it quite useful in preparing their lectures and examinations. Part I includes a brief theoretical treatment for each of the major areas of Continuum Mechanics (fluid mechanics, thermodynamics, elastic and inelastic solids, electricity, dimensional analysis, and so on), as well as the references for further reading. The bulk of Part II consists of about 1000 solved problems. The book includes bibliographical references and index.
