Principles of Mechanics

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PRINCIPLES OF MECHANICS by JOHN L. SYNGE. PREFACE TO THE SECOND EDITION: This edition differs in no essential way from the first. The principal revision occurs in Chap XIII, where the account of the motion of a particle in an electromagnetic field has been completely rewritten. The treatment of principal axes of inertia in Chap XI has been amplified, and some revisions have been made in the treatments of Foucaults pendulum, the spinning projectile, and the gyrocompass. The emphasis on units and dimensions has been increased by the inclusion in the earlier part of the book of a few short paragraphs, with references to the Appendix, where these matters are discussed in detail. A few additional exercises have been inserted, and numerous minor corrections have been made. We wish to thank all those readers who have contributed to the improvement of this second edition by their suggestions, arid, in particular, Professors L. Infeld, A. E. Sehild, and A. Weinstein. JOHN L. SYNGE BYRON A. GRIFFITH PITTSBURGH, PA. TORONTO, ONT. July, 1948. PREFACE TO THE FIRST EDITION: In a sense this is a book for the beginner in mechanics, but in another sense it is not. From the time we make our first move ments, crude ideas on force, mass, and motion take shape in our minds. This body of ideas might be reduced to some order at high school as crude ideas of geometry are reduced to order, but that is not the educational practice in North America. There is rather an accumulation of miscellaneous facts bearing on mechanics, some mathematical and some experimental, until a state is reached where the student is in danger of being repelled by the subject, as a chaotic jumble which is neither mathematics nor physics. This book is intended primarily for students at this stage. The authors ambition is to reveal mechanics as an orderly self contained subject. It may not be quite so logically clear as pure mathematics, but it stands out as a model of clarity among all the theories of deductive science. The art of teaching consists largely in isolating difficulties and overcoming them one by one, without losing sight of the main problem while attending to the details. In mechanics, the main problem is the problem of equilibrium or motion under given forces the details are such things as the vector notation, the kinematics of a rigid body, or the theory of moments of inertia. If we rush straight at the main problem, we become entangled in the details and have to retrace our steps in order to deal with them. If, on the other hand, we decide to settle all details first, we are apt to find them uninteresting because we do not see their connection with the main problem. A compro mise is necessary, and in this book the compromise consists of the division into Plane Mechanics Part I and Mechanics in Space Part II. These titles must, however, be regarded only as rough indications of the contents...