Download or read book A Variational Principle for Periodic Waves of Infinite Depth Primary Source Edition written by Ellen R. Gottlieb and published by . This book was released on 2013-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Download or read book A Variational Principle for Periodic Waves of Infinite Depth written by Ellen R. Gottlieb and published by Sagwan Press. This book was released on 2018-02-08 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book A Variational Principle for Periodic Waves of Infinite Depth Classic Reprint written by Ellen R. Gottlieb and published by . This book was released on 2015-08-05 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Variational Principle for Periodic Waves of Infinite Depth This paper deals with periodic waves on an ocean of infinite depth. The flow is assumed to be two-dimensional, incompressible, steady, and irrotational. The impossibility of the existence of an asymmetric wave is proved. This is accomplished through an application of Steiner symmetrization. Also discussed is the shape of possible periodic waves. Using the calculus of variations, we set up an extremal problem involving the kinetic energy, an area integral, and the potential energy. For waves of small amplitude the kinetic energy is shown to be a minimum if we fix the area and the potential energy. This is accomplished by showing the first variation to be zero and the second variation to be positive. Since the kinetic energy is closely related to the Dirichlet integral, this is a generalization of the Dirichlet principle. This result is applicable in showing the existence of periodic surface waves. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book A Variational Principle for Periodic Waves of Infinite Depth written by Ellen Ruth Gottlieb and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper deals with periodic waves on an ocean of infinite depth. The flow is assumed to be two-dimensional, incompressible, steady, and irrotational. The impossibility of the existence of an asymmetric wave is proved. This is accomplished through an application of Steiner symmetrization. Also discussed is the shape of possible periodic waves. Using the calculus of variations, an extremal problem is set up involving the kinetic energy, an area integral, and the potential energy. For waves of small amplitude the kinetic energy is shown to be a minimum if one fixes the area and the potential energy. This is accomplished by showing the first variation to be zero and the second variation to be positive. Since the kinetic energy is closely related to the Dirichlet integral, this is a generalization of the Dirichlet principle. This result is applicable in showing the existence of periodic surface waves. (Author).
Download or read book The Solitary Wave and Periodic Waves in Shallow Water Classic Reprint written by Joseph B. Keller and published by Forgotten Books. This book was released on 2018-10-10 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Solitary Wave and Periodic Waves in Shallow Water Numbers in square brackets refer to the bibliography at the end of the article. The theory given by Boussinesq involves a number of phys ical assumptions in addition to those of the basic hydro dynamical theory; it also leads to a differential equa tion for the wave profile. Both of these methods assume that the depth of the water is small compared to some horizontal dimension, and they might be interpreted as developments of the whole problem in powers of the ratio of the depth to some horizontal dimension, such as wave length. However, because these procedures are so unsys tematic, it is not clear that they are equivalent to such developments, nor to what order of approximation the so lutions obtained are valid. The method of proceeding to higher approximations is also obscure. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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 Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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Download or read book Ideal MHD written by Jeffrey P. Freidberg and published by Cambridge University Press. This book was released on 2014-06-26 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive, self-contained, and clearly written, this book describes the macroscopic equilibrium and stability of high temperature plasmas.
Download or read book Selected Water Resources Abstracts written by and published by . This book was released on 1979 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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Download or read book Vertical Magnetic Noise in the Voice Frequency Band Within and Above Coal Mines written by John Durkin and published by . This book was released on 1983 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Determining Vapor Density and Gaseous Diffusion Coefficients of Sb2S3 Using a Modified Transpiration Apparatus written by Brent W. Madsen and published by . This book was released on 1983 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
