1. COURSE MATERIALS
1. You should have a set of math tables. The four most generally used are listed below:
The first of these is quite serviceable and is also the least expensive; it is usually available at the GU Bookstore and Reiter's. The second of these is incorporated within the Handbook of Chemistry and Physics. The fourth of these is quite comprehensive and can be absolutely invaluable. Many working physicists own all four - as well as others that are less generally known. Several sets of math tables can also be found on the Reference Shelves of the Blommer Science Library.
2. You should have the use of a scientific calculator for this course. If you do not have a scientific calculator and plan to buy one, I recommend that you buy a programmable calculator. Since prices vary considerably, it is worthwhile to shop around.
3. When I instruct you to plot something, I generally intend that you produce a plot with Mathematica. However, should a plot produced by hand be called for, I expect you to use standard 1 mm graph paper. (Accounting paper is not graph paper.)
2. RESERVE MATERIAL
I will put books, articles, problem solutions, and other material, as appropriate, on reserve in the Science Library. I will also put selected materials in a notebook which will be available in the Department of Physics Office, 506 Reiss.
3. CLASS PERIODS
We will use the class periods primarily to:
1. discuss the main ideas, with an emphasis on the understanding of principles;
2. extend, elaborate, qualify, and apply the text material, as is appropriate;
3. work illustrative examples and problems, as is appropriate;
4. answer questions.
Students are strongly urged to read the assigned text material thoroughly and carefully before it is discussed in class, and to bring the text to class. This is most efficient for questions and discussion. The importance of this cannot be overemphasized.
4. EXAMINATIONS
There will be at least two examinations during the semester and a final examination. Examinations will be announced at least a week ahead of time.
5. HOMEWORK ASSIGNMENTS
Typically, there will be about four to six homework problems assigned each week. The due date will be specified for each problem; the problems are due by 7:00 pm on the due date. You should work on each homework problem within a day or two of its assignment - so that you have time to think about it, ask questions about it, and work on it. Your Professor will try to stay reasonably flexible when special circumstances - e.g., times of unusually heavy demands in other courses, problems that are particularly difficult, and other special circumstances - arise, but he will also generally discourage late homework.
6. GRADING
The final grades will be determined approximately as follows:
7. CAVEAT
All of the above is tentative and will be modified in whatever way appears appropriate. The class will of course, be informed of any and all changes at the earliest possible time.
8. QUESTIONS
One of your Professor's favorite comments goes something like "There are more good questions that go unasked, because the would-be questioner is afraid of looking foolish, than there are good questions asked.". The point is that serious thought-out questions are welcome. The odds are that if you have a legitimate question, others in the class have the same or a closely related question. Please don't hesitate; if you have what you feel to be a legitimate question, please speak up and ask it!
9. SOME GENERAL COMMENTS ON THIS COURSE
It is my job to help you achieve a basic appreciation and understanding of the subject matter of this course. To this end, I will try to facilitate helpful and constructive discussion in class, give homework assignments and examinations that are representative and fair, and be available for questions and discussion. I will challenge you to understand the subject matter of this course. I will also try to help you make your efforts effective. However, the bottom line is that . I estimate that it will take you about three hours of work outside of class for every hour in class to accomplish what I expect of you; of course, this is only a rough estimate and individual variations are to be expected.
10. INTRODUCTORY COMMENTS
The goals for this course are to help you learn enough classical mechanics to serve as a foundation for more advanced study in classical mechanics and other fields of physics, develop problem-solving skills, and apply problem-solving skills to realistic situations.
This course is intended to be a modern, intermediate-level introduction to classical mechanics. It is the first third-year-level course in the physics major curriculum. As such, the course will describe and develop modern methods and techniques that can be used in solving classical mechanics problems and, not incidentally, problems in other areas of physics. It is intended that this course serve as the foundation for advanced classical mechanics, electricity and magnetism, quantum mechanics, and statistical mechanics. Accordingly, oscillations, Newtonian gravitation, and Lagrangian and Hamiltonian mechanics will be emphasized. Although a substantial amount of mathematics will be used, the focus of the course will be on the treatment of physical systems.
The course will begin with a review of Newtonian mechanics (Chapter 2 of the text, hereafter referred to as M&T). This will be followed by the study of linear oscillations (Chapter 3 of M&T), some aspects of nonlinear oscillations (Chapter 4 of M&T), and Newtonian gravitation (Chapter 5 of M&T plus additional material). A heuristic introduction to Lagrangian and Hamiltonian mechanics will be given at the very outset of the course and a systematic treatment will be presented in the second half of the course (Chapter 7 of M&T.) Central force motion (Chapter 8 of M&T), the dynamics of rigid-body motion (Chapters 9 and 11 of M&T), and noninertial reference frames (Chapter 10 of M&T) will be considered to the extent that time allows.
A working familiarity with the topics covered in will be assumed. In particular, I expect everyone to be familiar with the basic aspects of Mathematica. Some problems will involve using Mathematica for plotting, algebraic manipulation, and programming. The emphasis in this course is on understanding the underlying physical concepts. Mathematica in particular and the computer in general are to be viewed as tools that help one solve problems and not as ends in themselves.
In many respects, classical mechanics is one of the FUN areas of physics. On the one hand, arguably, classical mechanics holds no profound, fundamental, conceptual mysteries. On the other hand, classical mechanics tests one's problem-solving skills and offers real challenges in understanding real-world systems. On the gripping hand, the results of classical mechanics can sometimes be put to experimental test without elaborate equipment. From this point of view, one should approach classical mechanics with, let us say, a certain amount of relish.
The statement that, " ... arguably, classical mechanics holds no profound, fundamental, conceptual mysteries ..." should not be interpreted as denying that classical systems sometimes behave in unexpected ways and present unsolved problems. The ongoing work on nonlinear and chaotic systems is rooted in classical mechanics. Fluid mechanics, which is one of the most active and challenging areas of all of physics, is based on little more than classical mechanics and thermodynamics. The old and essentially unsolved problem of convective motion is largely a problem in classical mechanics; its solution would have substantial implications in a number of areas, notably astrophysics. An understanding of planetary ring formation in all its varieties, which should require little more than an understanding of classical mechanics and the elastic properties of materials, is still not fully within our grasp. I could go on, but the point is clear. Let me close these comments by listing six references dealing with problems in classical mechanics that have been of recent interest in one way or another and that are fully accessible to students in this course.
1. M. G. Rushbridge, Am. J. Phys. 48, 146 (1980), "Motion of the sprung pendulum".
2. J. Lowell and H. D. McKell, Am. J. Phys. 50, 1106 (1982), "The stability of bicycles".
3. Bernard H. Schutz, Am. J. Phys. 52, 412 (1984), "Gravitational waves on the back of an envelope".
4. J. P. Wesley, Speculations in Science and Technology 10, 47 (1985), "Weber electrodynamics extended to include radiation".
5. Shannon Coffey, André Deprit, Etienne Deprit, and Liam Healy, Science 247, 833 (1990), "Painting the Phase Space Portrait of an Integrable Dynamical system".
6. William B. Base and Mark A. Swanson, Am. J. Phys. 58, 463 (1990), "The pumping of a swing from the seated position".
11. COURSE OUTLINE
1. Matrices, Vectors, and Vector Calculus (Chapter 1) * #
2. Newtonian Mechanics - Single Particle (Chapter 2) &
3. Oscillations (Chapter 3) §
4. Nonlinear Oscillations and Chaos (Chapter 4) £
5. Gravitation (Chapter 5) §
6. Some Methods in the Calculus of Variations (Chapter 6) #
7. Hamilton's Principle - Lagrangian and Hamiltonian Dynamics (Chapter 7) §
To the extent that time allows, we will also cover selected portions of Chapters 8 - 11 of the text.
* Chapter references are to the text.
# These chapters will be covered comparatively quickly, since the material should be somewhat familiar from .
& We will cover this chapter as quickly as is reasonably possible. It is, however, our "getting going" chapter, and so we may well spend three or four weeks on it.
£ This chapter will be covered comparatively quickly, primarily because it is arguably more specialized and less generally applicable than other material.
§ These three chapters are the heart of this course.