A Variational Principle for Periodic Waves of Infinite Depth (Classic Reprint)

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Excerpt from A Variational Principle for Periodic Waves of Infinite DepthMost of the results in this paper rest upon the investi gation of properties of M. Formulas for the first and second variations of M will be derived. The functional M and its first variation 6m will be important in showing the impossibility of the existence of certain asymmetric periodic waves. In the special case in which the wave is almost flat, we indicate in Chapter 4 how M might be used to set up an existence proof for periodic waves on an ocean of infinite depth. In particular we show that for a fixed area and a certain fixed potential energy.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.