COURSE INFORMATION Table of Contents Course Description Text Homework Exams Reading Journals Mathematics Used in Physics 321 Lecture Topics


Course Description
"Newton's laws applied to particles and systems of particles, including rigid bodies. Conservation principles and Lagrange's and Hamilton's equations."

The course is taught in a lecture format with weekly problem, experimental, and computer-project assignments. The course deals primarily with Newton's Second Law, which is a differential equation, and it is assumed that you have had a course and mastered the material in ordinary differential equations, linear algebra and multivariate calculus. Just in case, though, Chapter 3 of the text lists most of the differential equations that we will encounter in Physics 321 along with a description of the solutions. Some problems can only be solved using numerical methods and that is where we turn to a software marvel called ODE. ODE and the computer projects are described in Appendix A of the text. Computers are available for your use in N212 ESC. If you prefer, you might also use Mathematica or Maple for the computer projects if you have access to them.

Grades are determined by homework (50%), three examinations (15% each), and a reading journal (5%). (Click here to return to the Table of Contents)

Text

Text:	G. W. Mason, Mechanics	BYU Bookstore
Text (Optional):	Fowles/Cassiday, Analytical Mechanics (6th Ed.)	BYU Bookstore
	Saunders College Publishing

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Homework
Written homework should be neat and orderly and with problem numbers, references to page numbers in the book where the problems originate, references to Maple, etc., when used, etc.

Homework is ordinarily due at the beginning of class on Fridays except when a test falls on Friday, in which case the homework is due at the beginning of the next class period. (Occasionally, we may negotiate exceptions to the Friday rule.) Problems assigned on or before the Wednesday preceding Friday are then due. (See the calendar for problem and computer-project assignment dates.) Problems are graded on a 10 or 20 point scale (depending on difficulty or length) and computer projects are graded on a 20 point scale. Reading journals will be graded on a 5 point scale. (Click here to return to the Table of Contents)

Exams
Exams will emphasize derivations of the major theorems of mechanics (usually marked as "Theorems" in the text), the solution to homework/computer problems, and the lecture notes. (Click here to return to the Table of Contents)

Reading Journals
This business of writing is serious. Someone once said, "I write so I will know what I think." For some years I served in an administrative capacity at the university in which I often found myself faced with difficult issues. Time and again, I found myself alone with my word processor, writing to myself, as I tried to find solutions and needed to know what I really thought.

Similarly, you can't understand technical material that is laden with equations by just reading it and especially not by skimming it. You rapidly overload your circuits. The study of science then treats you very badly because it is hierarchical in structure, i.e., you always build on what went before and as soon as what went before starts to get mushy, there is only a limited distance you can go from where you are.

To know what they are thinking, many physicists I know write. They translate derivations into their own words and notation, they identify and note things that they don't understand, and try to pinpoint the difficulty, often in the process solving their own misunderstanding. I often try to reduce a long derivation to an outline of key steps. Many physicists fill notebook after notebook of reading notes that accompany their study. If you don't already have it, it is a good habit to get into. So, we will require that you keep a "reading journal."

Your "reading journal" must be an 8-1/2 x 11 inch notebook of at least 50 pages, bound on the left, and may not contain anything but your reading notes for this class. No looseleaf binders will be accepted. Your writing in this journal will be very informal. As you read the text and listen to lectures, summarize important sections by translating them into shorter versions in your own words. The reading journal will be a good place to write out for yourself the derivations and proofs of the theorems and major relationships that are the basis of mechanics. Write down what the equations mean. Identify and write down the conditions under which a given result may be used. Try to identify and categorize mathematical techniques that have general applicability beyond the specific problem that you may be using to illustrate the technique. Identify and write down things that don't seem clear. Can you pinpoint why a thing seems unclear? "Talk" to yourself! Look up things in other books so that you resolve the questions you pinpoint.

If you find yourself just copying things from the text or class notes into the reading journal, you are missing the point of the reading journal. Close the book so you can't copy! Now, how do you do? Reading journals should have stuff crossed out and notes added in the margin when you figure out something you didn't previously understand. If it is too neat, you are probably just copying. That is a waste of your time and of mine!

What I expect to see in the reading journal:

1. Important theorems, their proofs, derivations, digested lecture notes, notes accompanyhing your reading in the text, and notes from computer projects written in your own language.
2. Solutions of sample problems. (Sample test problems as you prepare for examinations, for example.) Solutions of exam problems you missed.
3. Attempts to select and organize the material on paper as evidence that you are selecting and organizing material in your own mind. You don't need to put everything in the course into the reading journal. There should be some evidence of winnowing the less important from the more important. What do you need to know if you were to have to derive Newtonian Mechanics for yourself from scratch some day when you are shipwrecked on a deserted island?
4. Evidence of ongoing, continuous effort to keep abreast of the course.
5. Evidence that you try to identify and pinpoint what you don't understand and evidence of attempts to remove the stumbling blocks that you have identified by referring to other textbooks, prerequisite course material or reference books.
6. Finally, a journal that you would not want to hand in to me just before an exam because you need it very much to help with your review.

What I do not expect to see in the reading journal:

1. Undigested lecture notes or text notes, just as you uncomprehendingly scribbled them in class or from the text.
2. Irrelevant or unimportant stuff.
3. Evidence that the journal had to be "caught up" at the last moment.
4. A journal that you would not need in reviewing for a comprehensive exam.

The journals are to be handed in with each exam, so bring them with you on exam days. (Click here to return to the Table of Contents)

Mathematics Used in Physics 321
Vector Calculus

1. Dot and Cross Products*
2. Derivatives of Vectors
3. Directional Derivative
   1. Chain Rule
   2. Gradient
4. Transformation of vectors between coordinate systems
5. Position, Velocity, Acceleration
6. Line integrals
7. Divergence and Curl

Generalized Coordinate Systems

1. Chain Rule
2. Generalized Basis Vectors
   1. Reciprocal Basis Vectors
   2. Metric Tensor
   3. Covariant and Contravariant Components
   4. Application to Acceleration
   5. Newton's Second Law in Covariant Form
   6. Lagrange's Equations

Ordinary Differential Equations

1. Separation of Variables
2. Linear Differential Equations
   1. First Order: Integration Factor
   2. Second Order:
      1. harmonic oscillator
      2. damped harmonic oscillator
      3. harmonically-driven harmonic oscillator
      4. damped, driven harmonic oscillator
      5. damped, periodically-driven harmonic oscillator
         1. Fourier series
      6. system of coupled harmonic oscillators
         1. Eigenvalue problem: eigenvalues and eigenvectors
3. Nonlinear equations
   1. Taylor's Series Solutions
   2. Jacobian Elliptic Functions
   3. Numerical Solutions

*Bolded topics are particularly important. The topics under Vector Calculus, the Chain Rule and Ordinary Differential Equations (Separation of Variables and Linear) are prerequisites for the course. (Click here to return to the Table of Contents)

Lecture Topics

Lecture Hour	Lecture Topic	Readings	Assignments
W 1-5-00	Intro/Vectors	Mas 3-10; Fow 6-15
F 1-7-00	Vectors	Fow 15-23	1-1,2,3
M 1-10-00	Derivatives of Vectors	Mas 11-14; Fow 23-24
W 1-12-00	Generalized Coordinates	Mas 16-21; Fow 24-36	Theorems into Journal
F 1-14-00	Generalized Coordinates	Mas 22-33; Fow 24-36	2-1,2,Theorems into Journal
W 1-19-00	Lagrange's Equations	Mas 34-36; Fow 391-404	2-3,4,5,6,7,8,9
F 1-21-00	Simple Harmonic Osc.	Mas 37-41; Fow 47-55,69-77
M 1-24-00	1-d Motion, Diff. Eqs.	Mas 186-189; Fow 55-61	4-1,2,3,4,5
W 1-26-00	ODE	Mas 148-161
F 1-28-00	TEST 1		Homework due Wed.
M 1-31-00	Damped SHO	Mas 41-42; Fow 83-92	4-6,7
W 2-2-00	Driven SHO	Mas 42-43; Fow 95-103	Com. CP 1 (SHO)
F 2-4-00	Fourier Series	Mas 43-44; Fow 125-126	Mas: 4-8,9
M 2-7-00	Four Series/Nonlinear	Mas 45-48; Fow 127-128	4-10,11
W 2-9-00	Gravity	Fow 202-209	4-12,13; CP 2 (Terminal Velocity)
F 2-11-00	3-d /Projectiles	Mas 58-64; Fow 145-149	4-14, 4-16
M 2-14-00	Spherical Pendulum	Fow 413-416	5-1,2,3
W 2-16-00	Lorentz Force	Fow 159-162	CP 4 (Driven SHO)
F 2-18-00	Catchup
T 2-22-00	Hamilton's Eqs.	Mas 64-68; Fow 427-430
W 2-23-00	Non-inertial Frames	Mas 11-14,70-72; Fow 169-180	6-1,2,3; CP 5 (Nonlinear SHO)
F 2-25-00	Non-int Lagrangian	Mas 72; Fow 181-184	6-4
M 2-28-00	Foucault Pendulum	Fow 185-196	6-5,6
W 3-1-00	Catchup	Fow 196-198	6-7,8; CP 11 (Noninertial)
F 3-3-00	TEST 2		Homework due Wed.
M 3-6-00	Interacting Particles	Mas 76-81; Fow 254-265
W 3-8-00	Central Force	Mas 82-85; Fow 209-212	8-1,2; CP 6 (Hysteresis)
F 3-10-00	Inverse Square Law	Mas 86-89; Fow 212-219
M< 3-13-00	Inverse Square Law	Fow 226-239	8-3,4,5,6,7
W 3-15-00	Collisions	Fow 282-292	CP 9(Gravitation)
F 3-17-00	Cross-sections	Mas 90-93; Fow 239-243
M 3-20-00	Cross-sections		8-11,12
W 3-22-00	Small Oscillations	Mas 44, 179-182; Fow 443-462	CP 10 (CM Coords.)
F 3-24-00	Small Oscillations	Fow 464-468
M 3-27-00	Rigid Bodies	Mas 97-101; Fow 300-305
W 3-29-00	Laminar Motion	Fow 322-327	9-1; 9-1, CP 8 (Small Oscills.)
F 3-31-00	Euler's Eqns./Prin. Axes	Mas 102-104; Fow 354-357	9-2,3
M 4-3-00	Principal Axes	Fow 334-344	9-4,5,6
W 4-5-00	Torque-free Rigid Body	Fow 356-360	CP 7 (Chaos)
F 4-7-00	Euler Angles, Top	Mas 105-106; Fow 364-370	9-7,8,9
M 4-10-00	Spinning Top	Fow 371-380	9-10
W 4-12-00	Calculus of Variations	Fow 391-396	CP 12 (Euler's Eqns.)

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