Computers in Physics Classical Mechanics Simulations Bruce Hawkins, Randall S. Jones, Richard A. Morrow, Susan R. McKay, and Wolfgang Christian Citation: Computers in Physics 10, 259 (1996); doi: 10.1063/1.4822397 View online: http://dx.doi.org/10.1063/1.4822397 View Table of Contents: http://scitation.aip.org/content/aip/journal/cip/10/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Classical Mechanics Am. J. Phys. 64, 191 (1996); 10.1119/1.18424 Classical Mechanics Am. J. Phys. 60, 1050 (1992); 10.1119/1.16990 Teaching classical statistical mechanics: A simulation approach Am. J. Phys. 49, 13 (1981); 10.1119/1.12620 Classical Mechanics Am. J. Phys. 36, 67 (1968); 10.1119/1.1974422 Classical Mechanics Phys. Today 5, 19 (1952); 10.1063/1.3067728
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 107.173.71.149 On: Thu, 22 Sep 2016 14:18:27
hand, there is some mismatch between the book and the diskettes. For instance, the program ISING is occasionally referred to as SPINS, and some of the input configurations of MANYPART have different names (for example, SPEC11A.MNP instead of SPEC11A. OAT) or are missing (I could not find SPEC16.DAT at all). As for runtime trouble, my fairly basic 486 did get hung up a few times-mostly when I chose mutually incompatible input parameters. When a program refuses to respond, pressing CTRL-ALT-DELETE brings up the usual Windows menu that lets the user choose between exiting by returning to the operating systems or a full reboot. I was always able to exit nicely back to Windows. Overall, the package makes for a nice addition to a standard lecture course, in the form of classroom demonstrations ofthe programs. A student who really wishes to learn with and from the programs (rather than treating them as little more than computer games) must already command a substantial amount of background knowledge. Thus, the programs would be excellent self-study guides for a student who has already taken the course. Yet I wonder how easy it would be to have students work through the programs in parallel to a lecture course. Would there be enough time in a standard one-semester course to provide the required background as well as introduce and connect the different programs? I would be willing to try .
Classical Mechanics Simulations Bruce Hawkins and Randall S. Jones Wiley, New York, 1995; ISBN 0-47154881-2; 152 pp., paper and diskette,
$37.95.
Reviewed by Richard A. Morrow
C
lassical Mechanics Simulations consists of six major programs. GENMOT describes the motion of a system with up to three degrees of freedom under various forces. ROTATE exhibits the rotation of a rigid body-in three dimensions, if the stereoscopic feature is mastered. COUPOSC ana-
Books Received Excel for Scientists and Engineers, Second Edition
Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
William Orvis, Sybex, Alameda, CA, 1996; ISB 0-7821-1761-9, 548 pp., Society for Industrial and Applied paper with diskette, $39 .99. Mathematics, Philadelphia, PA, 1996; ISB 0-89871 -366-8 586 pp., paper,
Mathematical Methods in Artificial Intelligence
Edward A. Bender, IEEE Computer Society Press, Los Alamjtos, CA, 1996' ISB 0-8 L86-7200-5 636 pp., cloth,
55.00.
$62.00.
Theory and Numerics of Ordinary and Partial Differential Equations
M. Ain sworth J. Lev ley, W. A. Light, and M. Marietta, eds., Oxford Practical ParaUel Programming University Press, New York, 1.995; Or gory Wilson, MIT Press, Cam- rSB 0-1 9-85 1J93-0, 333 pp., cloth, bridge, MA 1995; ISB 0-262-23186- $62.00. 7, 564 pp. , cloth, $50.00.
Pseudorandomness and Cryptographic Applications Michael Luby, Princeton Univer ity Press, Princeton, J, 1996; ISB 0691 -02546-0, 234 pp., paper, $24.95.
lyzes the motion of up to 10 objects coupled via up to 45 springs in one or two dimensions. ANHARM treats an anharmonic oscillator. ORBITER describes the planar motion of bodies, particularly in the solar system, interacting via gravitational forces. And, finally, COLLISION analyzes elastic collisions of two bodies interacting via a variety of central forces. Collectively, these programs cover the main topics treated in an undergraduate course in classical mechanics. I teach such a course to sophomores and use the text Analytical Mechanics by G. R. Fowles and O. L. Cassiday (Saunders, 1986). The programs are suitable for this course but, of course, are not keyed to any particular text. The most versatile program is GENMOT, which allows the solution of up to three second-order differential equations. These equations can be expressed in coordinates of the user's choice, including generalized Lagrangian coordinates. The solutions can be displayed in graphical form, tabular form, or even animation. The price to be
Accuracy and Stability of Numerical Algorithms icholas Highman, Society for Industrial and Applied Mathematics, Ph iladelphia, PA, 1996' ISBN 0-8987 1-3552, 688 pp., paper, $31.20.
paid for this versatility is a need for some programming to modify the Pascal source code that is included. Unfortunately I do not have the recommended Borland Turbo Pascal installed and so could not check these exceptional features ofGENMOT. The only features accessible to those without the Turbo Pascal compiler are some involving one-dimensional motion under certain driving forces: constant, velocity-dependent, Hooke's law, and periodic (in time). All were easy to run under user-defined initial conditions, and the animations were clear. The output could be displayed in several graphs that were easy to select. It is hard to tell, without doing some actual tests, how much this type of program would enhance students' understanding of physical concepts. It will not replace what I feel are some useful exercises for students in my course: solving numerically some simple equations
Richard A. Morrow is a professor ofphysics at the University of Maine, Orono, ME 04469. Email:
[email protected]
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 107.173.71.149 On: Thu, 22 Sep COMPUTERS IN PHYSICS, VOL. 10, NO.3, MAY/JUN 1996 259 2016 14:18:27
:BR
of motion using a programming language such as Basic or C++, a spreadsheet such as Microsoft Excel, or some specially designed software such as Matlab. This latter experience helps students to gain a better insight into differential equations at a time when many of them are concurrently studying differential equations in a mathematics class. The programs other than GENMOT are to be executed as is, with little opportunity to modify them. They offer choices that are easily selected but require no programming ability. Some programs take input and present output in SI units. This arrangement makes it convenient to use the results quantitatively. The exceptions are COLLISION and ORBITER. The former is formulated in dimensionless units and requires some effort to interpret in SI units. The latter, as might be expected for a solar-system simulation, uses units appropriate to the solar system. Chaos is well represented. The bulk of the chaos-related demonstrations are in ANHARM, which treats a driven anharmonic oscillator with several possible types of damping and potentials. Chaotic motion can also be generated in ORBITER and GENMOT. The animations are an exceptional feature of this packet. They ran rapidly on a 70-MHz Pentium-based PC and exhibited behavior that could in most cases be deduced analytically only with difficulty. Particularly striking in ROTATE was the instability of a rigid body freely rotating about an axis almost coincident with the principal axis corresponding to the intermediate moment of inertia. Another animation that particularly appealed to me was the scattering of particles from a potential in COLLISION. This program exhibited the orbits, followed by projectiles with increasing impact parameter, and displayed the differential cross-section. Such animations, present in all programs, have a strong visual impact and would be effective if used by the instructor as classroom demonstrations. A significant amount of student time would be required if all programs were used as the basis of assigned exercises. If the instructor is selective, though, the programs could be helpful in thoroughly exploring the physics and mathematics of a few topics .
Quantum Mechanics Simulations 1. R. Hiller, 1. D. Johnston, and D. F. Styer Wiley, New York, 1995; ISBN 0-47154884-7; 221 pp., paper and diskette, $37.95.
Reviewed by Dale Syphers
student on how to modify the programs to include simulations of their own choosing (here some understanding of Turbo Pascal is needed). The volume is best when looking at the intermediate and advanced aspects of undergraduate quantum mechanics such as time development, three-dimensional bound states, identical particles, and states in a one-dimensional lattice, where the material ranges from very good to excellent. The material at the most basic level, states in one-dimensional potentials and stationary scattering states, is good but should have had more thought put into what the introductory student needs in order to help develop the necessary intuition. In these basic areas, the software is set up to explore a particular situation but does not allow a direct visual comparison, on the same screen, of a different potential well. To obtain a comparison, students have to write down energy-level values and record situations when parameters are changed. Virtually all undergraduate QM courses cover this basic material, and only some will cover the intermediate and advanced topics mentioned above. As a whole, this is a good, solid unit that accomplishes much of what it hopes to, but more care in the design of the two introductory sections could make it the excellent resource it aspires to be. Additionally, as a review unit for first-year physics graduate students, it is excellent. +
uantum Mechanics Simulations is a useful complement to material taug t in undergraduate, and even firstyear graduate, courses in quantum mechanics (QM). Simulations designed to help students to build their QM intuition have often been used in these courses, but usually they are limited to one or two topic areas for which the instructor has had the time to write the appropriate code. This volume makes simulations available to assist student understanding of QM in eight separate areas: one-dimensional bound states, scattering in one dimension, quantum-mechanical time development, states in a one-dimensional lattice, three-dimensional bound states, quantal time development for a system of two particles, scattering states in three dimensions, and bound states in cylindrically symmetric potentials. Overall, the software is easy to use, with a user interface that any student in quantum mechanics should find transparent. The 220-page manual/book plays a variety of roles quite well. It is a solid guide to the software, with exercises for students to perform. It also discusses the quantum mechanics of each situation, providing many references directing students to appropriate texts for additional information, and is at its best when describing QM from the wave-mechanics approach rather than through matrices and generalized operators. The wave-mechanics pedagogical approach to QM may not be universal in undergraduate physics instruction, but it is something all students of QM should know, and this volume should fit well with most QM courses. In addition, it provides some information for the knowledgeable instructor or advanced
his wonderful collection of intuition-building simulations covers some core concepts in solid-state physics. It starts with a quote from Wigner: "It is nice to know that the computer understands the problem. But I would
Dale Syphers is an associate professor and chair of the physics department at Bowdoin College, Brunswick, ME 04011. E-mail: dsyphers@ bruin.bowdoin.edu
Christopher Levey is director of the Microengineering Laboratory at the Dartmouth College Thayer School of Engineering, Hanover, NH 03755. E-mail:
[email protected]
2
Solid State Physics Simulations Graham Keeler, Roger Rollins, and Steven Spicklemire Wiley, New York, 1995; ISBN 0-47154885-5; 192 pp., paper and diskette, $35.95.
Reviewed by Christopher Levey
T
Reuse of AIP content is subject theNO.3, terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 107.173.71.149 On: Thu, 22 Sep 260Publishing COMPUTERS IN PHYSICS, VOL.to10, MAY/JUN 1996 2016 14:18:27
