An Introduction to the Theory of Mechanics PDF
Preview An Introduction to the Theory of Mechanics
NUNC COGNOSCO EX PARTE TRENT UNIVERSITY LIBRARY AN INTRODUCTION TO THE THEORY OF MECHANICS Digitized by the Internet Archive in 2019 with funding from Kahle/Austin Foundation https://archive.org/details/introductiontoth0000bull_g0v4 AN INTRODUCTION TO THE THEORY OF MECHANICS by K. E. BULLEN M.A., Sc.D., F.R.S. Professor of Applied Mathematics in the University of Sydney SEVENTH EDITION CAMBRIDGE AT THE UNIVERSITY PRESS 1965 By the same author — AN INTRODUCTION TO THE THEORY OF SEISMOLOGY Cambridge University Press, Third Edition, 1963 SEISMOLOGY Methuen, 1954 PRINTED IN AUSTRALIA Wholly set up and printed in Australia by Simmons Limited for the publishers, Science Press, Marrickville, N.S.W. ONULP PREFACE TO THE SEVENTH EDITION This edition is the first in which a substantial revision of the original book has been undertaken. The immediate reason for the revision has been the demand by many teachers of Mechanics for a change-over from c.g.s. to m.k.s. units. The demand has been heeded to the extent that m.k.s. units are now given pride of place throughout the book, except in the chapters on Statics and Hydrostatics. At the same time, full provision has been made for readers who wish to become competent in the use of c.g.s. units. This was felt to be desirable because c.g.s. units continue to be used, not only in many school and university courses, but also in important branches of research. F.p.s. units are included with the same degree of emphasis as in earlier editions. In the worked and set exercises, pains have been taken to ensure that the reader who wishes may gain a mastery of all three unit systems, or, if he prefers, may concentrate on one or other of the m.k.s. and c.g.s. systems. This has required a substantial re-wording of many of the numerical exercises, with occasional minor numerical changes. With rare exceptions, the revised exercises correspond closely to those in earlier editions. The changes in units have made it necessary to re-set the entire book, and advantage has been taken of the occasion to improve the exposition in many places. In order to reduce inconvenience to teachers, pains have been taken, however, to preserve intact the original structure of the first sixteen chapters; in particular, the original section headings and numbers remain practically unaltered. PREFACE VI Chapter XVII has been appreciably enlarged, principally to include an introduction to some of the more immediate problems of extra¬ terrestrial mechanics—orbits of space vehicles, weightlessness, etc. It is hoped that the account will be found somewhat more reliable than accounts which have lately appeared in many elementary physics texts on these topics. Because of the increased size of Chapter XVII, it was decided to drop the Chapter XVIII of earlier editions. The following remarks are adapted from prefaces to earlier editions: The book assumes no prior knowledge of Mechanics or Calculus, but assumes that the reader will at least be starting to learn the calculus as he reads the book. Most of the earlier exercises can be solved without the calculus, but simple calculus is intermittently required in the theory and in later exercises. Vector methods up to scalar products and related topics are introduced in Chapter VI and applied in the following chapters on Dynamics. Vector products are introduced in Chapter XVII. The book contains all the vector theory needed for the topics it treats. The main emphasis is on Dynamics, which occupies most of Chapters III to XIII, but the book is designed so that readers who wish may start with Statics and Hydrostatics. These readers may proceed to Chapters XV and XVI after reading only a small number of the sections in earlier chapters; directions are given in §§ 10.4, 15.1A. Special efforts have been made to present the subject of Dynamics as Applied Mathematics—i.e. as a branch of Science in which mathe¬ matics is auxiliary to the central purpose of describing of a body of obser¬ vational evidence about the natural world. Thus, so far as seems reason¬ able in an elementary book, attention is given to questions of inductive inference as well as logical soundness. The former questions are dis¬ regarded by many mathematical writers on Mechanics, and the latter, often blatantly, by physicist and other writers. I am of course aware that very much more can be written on the inductive side than appears in this book, and in particular on Newton’s laws of motion, but there are limits to what can be reasonably attempted in a first course.
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