Springer-Verlag Berlin, 1987. — 583 p. — ISBN 3-540-16189-9.Authors: Myshkis A.D., Babskii V.G., Kopachevskii N.D., Slobozhanin L.A., Tyuptsov A.D.This book deals with the behavior of a liquid in zero-gravity or conditions close to it. The surge of interest in zero-gravity problems stems from the progress attained in the field of spaceflight, where such conditions can be attained for long periods of time. Hence the very term "zero-gravity" has a romantic halo about it: although spaceflights have become an accepted fact of life, they are not by any means everyday occurrences. Each new spaceflight involves the best that the present-day level of scientific and technical advancement can offer, and may be considered as a quest for the unknown.This book is devoted entirely to the mathematical theory of fluid mechanics under zero-gravity or, to be more precise, to an analysis of the problems of fluid mechanics under zero-gravity from the point of view of applied mathematics. This theory has been developed quite significantly over the last few years and has proved to be much richer in content than had originally been expected. This book deals with the statics and small movements of a liquid (roughly speaking, with nonlinear statics and linear dynamics on a nonlinear static background), since the theory of considerably nonlinear movements of a capillary liquid has been worked out quite inadequately so far. The problems discussed are of interest to a wide range of readers. Engineers in the field of space technology and specialists in mechanics interested in the applications of problems will be excited by the qualitatively new aspects in the behavior of a liquid in zero- and near-zero-gravity, the corresponding methods of computation, and the results of calculations presented in the form of numerous graphs and tables. Researchers in mathematics and theoretical branches of mechanics will be interested in the possibility of formulating new mathematical problems admitting a direct physical interpretation and requiring methods of functional analysis and mathematical physics, which, up to now, have not been worked out in detail. The book consists of a Foreword, Introduction (Chap. 1), and eight chapters divided into three parts: Part I (Chaps. 2-4) deals with problems of hydrostatics, Part II (Chaps. 5 - 7) is devoted to the theory of small oscillations, and Part III (Chaps. 8, 9) describes convection in zero-gravity. Separate lists of references have been compiled: one for the Introduction and Preface, and one following each part of the book.Introduction. Statics. Equilibrium Shapes of a Liquid. Stability of Equilibrium States of a Liquid. Bifurcation of Equilibrium States. Small Oscillations. Small Oscillations of an Ideal Liquid. Methods of Calculating Linear Oscillations of an Ideal Liquid. Linear Oscillations of a Viscous Liquid. Convection. Convection in a Self-Gravitating Liquid. Thermocapillary Convection.
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