This book is concerned with the purely kinematical properties of the vorticity vector in hydrodynamics (except for some parenthetical remarks on the dynamics of the problem), and the author concentrates on the general aspects of the subject rather than on particular applications. ... Nothing dies in Mathematics and the day may come when even some of the seemingly "useless" parts of the book will find their application. In any case the treatise is of great value as a contemporary "handbook" on the subject. Also, the author's great erudition in the history of Hydrodynamics should not mask the fact that a considerable number of his own contributions is included in the work under review.
Though called an "introduction" to some of the corresponding Euler volumes in this series, this is really the first modern scholarly treatise on the theory of deformable solids: Todhunter and Pearson's and other older works dealing with this topic will henceforth have a place only in the historiography of the subject. Here, for the first time, the immense achievements of James Bernoulli and Euler himself in this field (hitherto relatively neglected) are given just credit.
Its principal aims were to replace the conceptual, terminological, and notational chaos that existed in the literature of the field by at least a modicum of order and coherence, and second, to describe, or at least to summarize, everything that was both known and worth knowing in the field at the time. Inspecting the literature that has appeared since then, we conclude that the first aim was achieved to some degree. Many of the concepts, terms, and notations we introduced have become more or less standard, and thus communication among researchers in the field has been eased. On the other hand, some ill-chosen terms are still current. ... We believe that the second aim was largely achieved also. We have found little published before 1965 that should have been included in the treatise but was not.
The four volumes of reprints are designed to reflect the resurgence of continuum mechanics in the past few years. Nothing published earlier than 1945 is included, and nothing later than 1961. The contents of the four volumes are connected, some-times loosely and sometimes closely, with each other, so that the division is somewhat arbitrary. ... Like other new fields in the past, the new continuum mechanics attracted little notice at first. The forty-nine papers reprinted here are by only eighteen authors, of whom six are responsible for thirty-six of the papers.
This book is based on a series of lectures given by the author at Syracuse University in 1965. The lectures are concerned with classical continuum mechanics, i.e., no couple stresses, etc. ... Amongst the recent expositions of the foundations of continuum mechanics, this book occupies a privileged position. The reviewer does not hesitate to recommend this book to anyone giving or attending a course on continuum mechanics.
This volume is a collection of essays on the history of mechanics, some already published or revised from the author's earlier papers.
The book contains a good deal of classical material but the emphasis is very much on the more recent developments, inspired by the author ...
The aim of this book is to reinstate the theory of (nonlinear) elasticity as a branch of mathematics after its long use mainly in applications. The authors, by fully emphasizing the mathematical structure of the theory, admirably succeed in their intention and as a result it is to be hoped that many more mathematicians will be attracted to the subject. ... This is a lucid account, highly recommended to anyone interested in acquiring a mathematical insight into elasticity.
I do not think it possible to write the history of a science until that science itself shall have been understood, thanks to a clear, explicit, and decent logical structure. The exuberance of dim, involute, and undisciplined historical essays upon classical thermodynamics reflects the confusion of the theory itself. Thermodynamics was born in obscurity and disorder, not to say confusion, and there the common presentations of it have remained. With this tractate I aim to provide a simple logical structure for the classical thermodynamics of homogeneous fluid bodies. Like any logical structure, it is only one of many possible ones. I think it is as simple and pretty as can be. That this tractate is a long one, results from its triple scope: (1) Conceptual: for those already expert in thermodynamics, to show how all the concepts of the traditional, elementary theory can be derived from simple and natural assumptions about heat engines, developed by simple and rigorous mathematics. (2) Pro-Historical: for those who would study the pioneer researches, by logical analysis to reveal the features of principle common to Carnot's thermodynamics and Clausius', and to discern the irreconcilable differences of principle between them. (3) Paedagogical: for those who wish to learn a clean elementary thermodynamics so as to teach it to beginners. I have presented the theory in such a way that this text could be made (and indeed it already has been made) the basis of a first course in thermodynamics for gifted and thoughtful undergraduates, with the proviso, nowadays difficult of fulfilment, that they master the elements of differential and integral calculus, not merely its lingo. For this reason I have included detailed proofs of propositions which to physicists and engineers may seem so obvious as to need no proof, to mathematicians so simple that anyone can prove them.
In writing a textbook of continuum mechanics at this time I imitate the example of Lagrange in several ways. My book offers merely a selection from the wondrous harvest of the last few decades; leaving much else unmentioned, it bases that selection on criteria of naturalness, ease, and subsumption to a general method and conceptual frame. Thus it is a short book, designed for readers who know already that applications to further cases are numberless and possibilities for further mathematical study infinite.
The contents indicate the first peculiarity of the book: its encyclopaedic nature. Two other peculiarities should be noted which distinguish the book among the monographs and reviews related to the given topic. One is its historicism. The authors reach back to the papers of the founders of the kinetic theory: Maxwell and Boltzmann. This gives the right retrospective understanding of problems which is, from the reviewer's point of view, extremely important for modern kinetics. The second peculiarity is related to the style of the book. Throughout the authors clearly distinguish the "physical" postulates and hypotheses from their mathematical consequences. This makes the book naturally "readable" for a mathematician.
The book compares the history of thermodynamics with a rational, fully mathematized and uninterrupted organization of this discipline as obtained from hindsight and only recently completed by the author. Thus the historical course of events appears as a tragicomedy, partly as a "murky swamp of darkness". ... The reader must constantly go back and forth between the actors on the stage, who, of course, do not yet know the solution of the knots, and Truesdell, who does. Mottos from Dante concerning smoke, stench, crowding, impenetrable thickets and overgrown fields, but also of light and order, accompany the text. One can learn a lot from this book about the relationship of logically mathematical order and physical imagination or intuition, which is allowed to indulge in some brilliant carelessness, i.e., one can learn about the "complementarity of clarity and truth" (Bohr).
In this long and peculiar book the fugitive idiot (p. 589) author provides a selection from his many previous publications, some reprinted elsewhere already, many rewritten in a minor or major way; in addition, five items appear for the first time. ... it is hard to imagine any sort of person with interests appropriate to the ensemble of this inchoate heterogeneity: overall the book conveyed to the reviewer an impression of self-indulgence.
This book contains three essays, based on lectures given in 1985, on Leonardo da Vinci, Galileo, and on the role of experiments in the history of science. All are thought-provoking and refreshed with current scholarship. ... The book, well illustrated and written in its author's familiar trenchant style, shows him now more than ever opposed to the rituals of academe.
This book presents an exposition of the mechanical response of fluids, in a unified treatment ranging from the most general fluid models used to describe new materials to those for air and water. ... This book serves several purposes. It is an important reference which presents various classes of fluids within the context of the general theory of fluids. It contains many recently determined solutions to the equations of motion for nonlinear fluids and uses these solutions to evaluate the fluid models. In addition, the authors provide many interesting comments about historical development, important discussions about the interpretation of fluid models as exact vis-a-vis approximations within a more exact theory and comments about modern developments in mathematical studies of the governing equations of motion. The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments. This is an excellent book which is highly recommended to students and researchers in fluid mechanics.
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