Topics in Classical Physics

Fall 2007

Go to **home page for Ph106b**

**Course description: **A course in
classical mechanics. Topics include calculus of variations and principle of least
action, Lagrangian and Hamiltonian mechanics, central
force motion, rigid bodies, small oscillations, canonical transformations,
Hamilton-Jacobi theory, action-angle
variables. (The first half of Ph 106b will be an introduction to chaotic
behavior in classical dynamics.)

**Class meetings**:
Tuesdays and Thursdays 10:30-11:55 in 107

**Feedback:** If you want to send a
comment about the course, click here.

**Instructor:
**John Preskill
, 448 Lauritsen Laboratory, X-6691, email: preskill@theory.caltech.edu

Teaching assistants:

Hee Joong Chung, email: hjchung@caltech.edu

Haekong Kim, email: hkkim@caltech.edu

**Grading:** Grades will be based
on weekly problem sets (30%), a midterm (30%), and a final exam (40%).

**Homework: **Homework will be
posted here on Thursday, and will be due in class the following Thursday. If
your homework will be late for a good reason, you may request an extension from
the grader. Late homework will be accepted for half credit up until one week
after the due date (no credit if your assignment is more than one week late).

**Lectures **(tentative schedule)**:**

Oct. 2: Calculus of variations, brachistochrone problem.

Oct. 4: Constrained extremization, Lagrange
multipliers.

Oct. 9: Principle of Least Action, the Lagrangian,
holonomic constraints.

Oct. 11: Symmetries and conservation laws.

Oct. 16: Action of an electrically charged particle, the two-body problem.

Oct. 18: Kepler problem, differential cross section.

Oct. 23: Rutherford scattering, rigid body kinematics.

Oct. 25: Angular velocity, fictitious forces, inertia tensor.

Oct. 30: Euler equations, torque-free precession, stability of uniform
rotation, Euler angles.

Nov. 1: Rigid body with one point fixed,
the gyroscope.

Nov. 6: Sleeping top, coupled
oscillators.

Nov. 8: Normal modes, linear molecule.

Nov. 13: Forced and damped oscillations.

Nov. 15:

Nov. 20: Maupertuis principle, adiabatic invariance
of the action variable, virial theorem, Poisson
bracket.

Nov. 27: Poisson’s theorem, Liouville’s
theorem, canonical transformations.

Nov. 29: Generating functions, infinitesimal canonical transformations, symmetries
and conservation laws as properties of flows in phase space.

Dec. 4: Canonical invariants, Hamilton-Jacobi theory.

Dec. 6: Integrable
systems and action-angle variables.

**Homework assignments:**

(Graded homework will be returned in class, and thereafter will be available
for pickup outside 448 Lauritsen.)

Read Goldstein Chapters 1 and 2. (You may skim Sec. 1.4 through 1.6.)

Problem Set 1, due

Problem Set 2, due

Read Goldstein Chapter 3.

Problem Set 3, due 25 October 2007: Conservation laws and central force motion
(PDF).
Solution: PDF

Read Goldstein Chapter 4 and Chapter 5 through Sec. 5.6.

Problem Set 4, due 1 November 2007: Scattering, fictitious forces, and
torque-free precession (PDF).
Solution: PDF

Read Goldstein Chapter 5 from Sec. 5.7 and Chapter 6.

Problem Set 5, due 15 November 2007: Tops and small oscillations (PDF).
Solution: PDF

Read Goldstein Chapter 8.

Problem Set 6, due 29 November 2007:

Read Goldstein Chapters 9, 10, and Sec. 12.5 (or Sec. 11.7 of the 2^{nd}
edition). Solution: PDF

Problem Set 7, due

**Exams:**

Midterm: available 1 November and due 8 November. Covers all material through
Problem Set 4.

Cover page with midterm instructions: PDF.
(You may open this now.)

Midterm exam: PDF.
(Open only when you are ready to take the exam.)

Midterm solution: PDF.
Hee Joong graded problem 1
and Haekong graded problem 2. The mean was 76 and the
standard deviation was 21.

Final: available 6 December and due 13 December. The final covers everything in
the course, but emphasizes the material from after the midterm (including
normal modes, canonical transformations and Hamilton-Jacobi
theory).

Cover page with final exam instructions: PDF.
(You may open this now.) Note that, in response to popular demand, you are
permitted to consult Prof. Golwala’s on-line notes.

Final exam: PDF.
(Open only when you are ready to take the exam.)

Final exam solution: PDF.
Hee Joong graded problem1, Haekong graded problem 2,
Denis graded problem 3, and John graded problem 4. The median was
181/200. The exams are available for pickup outside 448 Lauritsen.

**Grades:**

Grades for Ph106a were determined by the formula: 0.3*(HW) + 0.3*(Midterm) +
0.4*(Final), or 0.5*(HW) + 0.5*(Final), whichever was higher.

The ranges for letter grades were:

A+ 95-100

A 90-94

A- 85-89

B+ 80-84

B 70-79

B- 60-69

C+ 50-59

C 40-49

There were 8 A+’s, 15 A’s, 17 A-‘s, 6 B+’s, 5 B’s, 2 B-‘s, 1 C (Total=54)