Lagrangian Review Problems (due Friday January 31): Problems LR-1 and LR-2.
Problem Set 1: Problems 8-1 (note that we cannot now take R = 0), 8-2 (make the change of variable to u = l/r before trying to integrate), 8-5 (assume a mass m orbiting a much larger mass M to do the calculation; then explain why the "equivalent one-body problem" would lead to the same result even if m and M (or m1 and m2) were similar in magnitude), 8-7 (in order to calculate the time averages, first use Lagrange's equations to find the general solution for x(t), y(t), and z(t)).
For Problem 2 you may use Mathematica to do the integral. However, please follow these ground rules when using Mathematica to carry out any part of a calculation for you: first put the integral in dimensionless form and make any other obvious changes of variable which simplify the calculation; then either print out the output from Mathematica or copy it verbatim into your solution; and remember that even if you use Mathematica to do part of a problem for you, you should make a full writeup of your solution to the problem, including diagram, discussion of the problem, details of solution, and discussion of the result.
Problem Set 2: Problems 8-10, 8-18, 8-19, and 8-26
Problem Set 3: Problems 8-32, 8-36, 8-41, 9-4, 9-5.
Problem Set 4 (due Wednesday Feb. 26): Problems 9-10, 9-11, 9-19.
Problem Set 5 (due Wednesday March 12): Problems 9-32, 9-44, 9-50, 10-1, 10-6.
Problem Set 6 (due Wednesday March 26): Problems 10-4, 10-9, 10-12, 1-4 (use the Einstein summation convention in part (a)), 1-23 (use the "epsilon-killer" identity, eq. (1.78)).
Problem Set 7 (due Wednesday April 2): Problems 1-15, 1-24, 11-2, 11-6, 11-12, 11-16
Problem Set 8 (due Wednesday April 9: Problems 11-5, 11-17, 11-20, 11-22, 11-23, and 11-28
Problem Set 9 (due Wednesday April 16): Problems 11-24, 11-26, 11-29, 12-1, 12-4 [start with equations 12-10, and take the real part before calculating T and U; for compactness, define B1 = B1+ + B1-, B2 = B2+ + B2-].
Problem Set 10 (due Wednesday April 30): Problems 12-6 [Discuss is a bit open ended; try to guess or calculate as much as you can about the resonant frequencies and normal modes], 12-16 [use two angles as generalized coordinates], 12-17, 12-22, 12-24.
Problem Set 11 (due Wednesday May 7): Problems 14-2, 14-4, 14-9, 14-10, 14-13, 14-20
Problem Set 12 (due Wednesday May 14): Problems 14-24, 14-26, 14-27, 14-31, 14-37