Errors in Goldstein's Classical Mechanics - Feb., 2003

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/238984277 Errors in Goldstein's Classical Mechanics Article in American Journal of Physics · February 2003 DOI: 10.1119/1.1533731 CITATIONS 5 READS 743 1 author: Martin Tiersten City College of New York 15 PUBLICATIONS 125 CITATIONS SEE PROFILE Available from: Martin Tiersten Retrieved on: 12 November 2016 Errors in Goldstein’s Classical Mechanics Martin Tiersten Citation: American Journal of Physics 71, 103 (2003); doi: 10.1119/1.1533731 View online: http://dx.doi.org/10.1119/1.1533731 View Table of Contents: http://scitation.aip.org/content/aapt/journal/ajp/71/2?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Teaching classical mechanics using smartphones Phys. Teach. 51, 376 (2013); 10.1119/1.4818381 Operator methods in classical mechanics Am. J. Phys. 70, 951 (2002); 10.1119/1.1485713 Classical Mechanics, 3rd ed. Am. J. Phys. 70, 782 (2002); 10.1119/1.1484149 Classical and quantum mechanics of a particle on a rotating loop Am. J. Phys. 68, 1128 (2000); 10.1119/1.1286427 Introduction to Classical Mechanics, 2nd ed. Am. J. Phys. 68, 390 (2000); 10.1119/1.19449 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 47.17.215.178 On: Mon, 14 Dec 2015 21:33:55 THE DISORDER METAPHOR The metaphor ‘‘disorder’’ for entropy is more than 100 years old. Already in1882, Hermann von Helmholtz character-ized entropy as ‘‘Unordnung.’’ 1W a sh et h e first? Who actually introduced the meta-phor and when? We would appreciate anyreferences prior to 1882. And because thismetaphor is controversial and potentiallymisleading, who was the first to discuss itsshortcomings? 1Hermann Helmholtz, Wissenschaftliche Abhan- dlungen ~Barth, Leipzig, 1883 !, Vol. 2, p. 972. The paper, entitled ‘‘The thermodynamics ofchemical processes,’’ was reprinted from theSitzungsberichten der Akademie der Wissen-schaften zu Berlin for February 2, 1882. Helm-holtz wrote as follows: ‘‘Unordered motion, incontrast, would be such that the motion of eachindividual particle need have no similarity tothat of its neighbors. We have ample ground tobelieve that heat-motion is of the latter kind,and one may in this sense characterize themagnitude of the entropy as the measure of thedisorder @literally, of the ‘‘Unordnung’’ #.’’ Ralph Baierlein Department of Physics and Astronomy Northern Arizona University Flagstaff, Arizona 86011 Electronic mail: [email protected] Clayton A. Gearhart Department of Physics Saint John’s University Collegeville, Minnesota 56321-3000 Electronic mail: [email protected] ERRORS IN GOLDSTEIN’S CLASSICAL MECHANICS The review1of the 3rd edition of Gold- stein’sClassical Mechanics2~with co- authors Poole and Safko !in the July 2002 issue of AJP elicits the following com-ments. Despite this book’s having playedthe role for so long of ‘‘...the acknowledgedstandard text for the introductory Classical Mechanics course in graduate level physicscurricula throughout the U.S.’’ ~as stated in the new Preface !, some serious errors have remained through all three editions, withone of the worst now promoted to the frontcover. The diagram on the front cover~which also appears on p. 80 !is supposed to represent the nature of attractive central-force orbits for bounded motion; the mo-tion depicted is, however, an impossibleone. Whereas the actual path at a turningpoint must always be concave toward thecenter of force, the diagram in question hasthe orbit convex toward the center of forceat some of the turning points ~where the orbit is tangent to the inner circle !. This path is clearly impossible. The same erroris repeated in Fig. 3.13 on p. 91. ~For a correct version of this kind of motion, seethe diagram on the cover of the 4th editionofClassical Dynamics by Marion and Thornton. 3! I believe that at least a part of the reason that this egregious error has not beenwidely noticed in the 50 1years of use of this text is the deplorable fact that virtuallyall mechanics texts have for a long time notincluded any treatment of normal and tan-gential components of acceleration ~often called ‘‘arc coordinates’’or ‘‘intrinsic coor-dinates’’ !, restricting their treatments to Cartesian, cylindrical, and spherical coordi-nates. Consequently, the relation F n 5mv2/R, whereRis the radius of curva- ture andFnis the normal component of the force, relating the component of force in toward the center of curvature to the accel-eration v2/Rin that direction, appears ~amazingly !not to be widely known among physicists ~and, even when it is known, it is not at the forefront of their awareness !. Be- cause an attractive force is always directedin toward the center of force, the directiontoward the center of curvature at the turn- ing points must be toward the center offorce. Although this error has persisted in this text for more than 50 years, its remainingpresence on the front cover is surely intol-erable and should be corrected as soon aspossible. 1Stephen R.Addison, ‘‘Review of Classical Me- chanics,’’ 3rd ed., by Herbert Goldstein, Charles Poole, and John Safko, Am. J. Phys.70, 782–783 ~2002!. 2Herbert Goldstein, Charles Poole, and John Safko,Classical Mechanics ~Addison–Wesley, New York, 2002 !, 3rd ed. 3Jerry B. Marion and Stephen T. Thornton, Classical Dynamics of Particles and Systems~Saunders, Fort Worth, 1995 !, 4th ed. Martin Tiersten Department of Physics The City College, CUNY New York, New York 10031 AUTHORS’ REPLY We wish to thank Professor Martin Tier- sten for informing us about errors in threefigures of central force motion orbits thathave persisted through all three editions ofthe Goldstein Mechanics text.We are in theprocess of listing errata for the third editionon our Web site ^http://astro.physics.sc.edu/ Goldstein/ &, and we will include there some brief comments on orbits arising from cen-tral force motion. We would appreciate it if Professor Tier- sten and other members of the physicscommunity would send us any other errorsthat they notice so that we can list them onthe Web site and correct them in futureprintings. John L. Safko Charles P. Poole, Jr. Department of Physics and Astronomy University of South Carolina Columbia, South Carolina 29208LETTERS TO THE EDITOR Letters are selected for their expected interest for our readers. Some letters are sent to reviewers for advice; some are accepted or declined by the editor without review. Letters must be brief and may beedited, subject to the author’s approval of significant changes.Although some comments on publishedarticles and notes may be appropriate as letters, most such comments are reviewed according to aspecial procedure and appear, if accepted, in the Notes and Discussions section. ~See the ‘‘Statement of Editorial Policy’’ in the January issue. !Running controversies among letter writers will not be published. 103 103 Am. J. Phys. 71~2!, February 2003 http://ojps.aip.org/ajp/ © 2003 American Association of Physics Teachers This article is copyrighted as indicated in the article. 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