Homework Problems
Reading Assignment #1:
1. Dragt
a) Sections 1.1 through 1.4 of Chapter
1 (Introductory Concepts).
b) Introductory paragraphs, Sections 2.1 through 2.4, and Section 2.7 of Chapter 2 (Numerical integration). Also Appendix B (Computer Programs for Numerical Integration).
c) Sections 1.1 through 1.5 in Chapter
1 (ELEMENTARY CONCEPTS) of Classical Mechanics.
2. Goldstein
a)
Sections
1.1 through 1.3, and Section 3.4.
b)
Section
11.8. Note that, contrary to what
Goldstein says, the quantity a is as universal as d.
c)
Pages
503 through 505 of Section 11.6.
Equation 11.26 is called the Henon map. Here the quantity a is
related to the phase advance. The
ranges for x,y should be ±´.
1.
(10
pts) D1.2.1 [problem 2.1 in Chapter 1 (Introductory Concepts) of Dragt].
2.
(20
pts) D1.2.2
3.
(10
pts) D1.2.3
4.
(40
pts) D1.2.4
5.
(10
pts) D1.2.5
6.
(30
pts) D1.2.6
7.
(10
pts) D1.3.1
8.
(10
pts) D1.3.2
9.
(10
pts) D1.3.3
10.
(10
pts) D1.3.4
11.
(10
pts) D1.3.5
12.
(10
pts) D1.3.6
Reading Assignment #2:
1. Dragt
a) Chapter 3 (LAGRANGIANS AND
HAMILTONIANS)
2. Goldstein
a)
Sections
1.4 through 1.6.
b) Sections 2.1 through 2.3
13.
D2.2.1
[problem 2.1 in Chapter 2 (Numerical Integration) of Dragt].
14.
D2.3.1
15.
D2.4.1
16.
D2.4.2
17.
D2.4.3
18.
D2.4.4
19.
D2.4.6
20.
DCM1.3
[problem 3 in Chapter 1 (ELEMENTARY CONCEPTS) of CLASSICAL MECHANICS by Dragt].
21.
DCM1.7
22.
DCM1.10
23.
DCM1.11
24.
DCM1.12
Each problem worth 10
points
Reading Assignment #3:
1. Dragt
a)
Handout
on Variational Calculus
b)
Handout
on the Central Force Problem
2. Goldstein
a)
Sections
2.5 through 2.7
b) Sections 3.1 through 3.6
Problem Set 3 due Monday, 9/30/02
25.
(10
pts) DCM1.15 [problem 15 in Chapter 1 (ELEMENTARY CONCEPTS) of CLASSICAL
MECHANICS by Dragt].
25.
(10
pts) DCM1.16
26.
(20
pts) DCM1.18
27.
(20
pts) DCM1.21
28.
(20
pts) DCM1.22 (Schwarz's inequality is given as THEOREM 7 of Dragt NOTES ON
VECTORS AND VECTOR SPACES.)
29.
(10
pts) G1.8 (problem 8 in Chapter 1 of Goldstein).
30.
(10
pts) G1.9
31.
(10
pts) G1.10
32.
(10
pts) G1.22