PHY 711 Classical Mechanics and Mathematical Methods

MWF 10 AM-10:50 AM OPL 103 http://www.wfu.edu/~natalie/f20phy711/

Instructor: Natalie Holzwarth Office:300 OPL e-mail:natalie@wfu.edu

Course schedule

(Preliminary schedule -- subject to frequent adjustment.)
DateF&W ReadingTopic AssignmentDue
1 Wed, 8/26/2020Chap. 1 Introduction #18/31/2020
2 Fri, 8/28/2020Chap. 1 Scattering theory #29/02/2020
3 Mon, 8/31/2020Chap. 1 Scattering theory #39/04/2020
4 Wed, 9/02/2020Chap. 1 Scattering theory
5 Fri, 9/04/2020Chap. 1 Scattering theory #49/09/2020
6 Mon, 9/07/2020Chap. 2 Non-inertial coordinate systems
7 Wed, 9/09/2020Chap. 3 Calculus of Variation #59/11/2020
8 Fri, 9/11/2020Chap. 3 Calculus of Variation #69/14/2020
9 Mon, 9/14/2020Chap. 3 & 6 Lagrangian Mechanics #79/18/2020
10 Wed, 9/16/2020Chap. 3 & 6 Lagrangian & constraints #89/21/2020
11 Fri, 9/18/2020Chap. 3 & 6 Constants of the motion
12 Mon, 9/21/2020Chap. 3 & 6 Hamiltonian equations of motion #99/23/2020
13 Wed, 9/23/2020Chap. 3 & 6 Liouville theorm #109/25/2020
14 Fri, 9/25/2020Chap. 3 & 6 Canonical transformations
15 Mon, 9/28/2020Chap. 4 Small oscillations about equilibrium #1110/02/2020
16 Wed, 9/30/2020Chap. 4 Normal modes of vibration #1210/05/2020
17 Fri, 10/02/2020Chap. 4 Normal modes of vibration
18 Mon, 10/05/2020Chap. 7 Motion of strings #1310/07/2020
19 Wed, 10/07/2020Chap. 7 Sturm-Liouville equations #1410/09/2020
20 Fri, 10/09/2020Chap. 7 Sturm-Liouville equations
21 Mon, 10/12/2020Chap. 7 Fourier transforms and Laplace transforms
22 Wed, 10/14/2020Chap. 7 Complex variables and contour integration
23 Fri, 10/16/2020Chap. 5 Rigid body motion
24 Mon, 10/19/2020Chap. 5 Rigid body motion #1510/21/2020
25 Wed, 10/21/2020Chap. 8 Elastic two-dimensional membranes #1610/23/2020
26 Fri, 10/23/2020Chap. 5,7,8 Review #1710/28/2020
27 Mon, 10/26/2020Chap. 9 Mechanics of 3 dimensional fluids #1810/30/2020
28 Wed, 10/28/2020Chap. 9 Mechanics of 3 dimensional fluids
29 Fri, 10/30/2020Chap. 9 Linearized hydrodynamics equations #1911/02/2020
30 Mon, 11/02/2020Chap. 9 Linear sound waves #2011/04/2020
31 Wed, 11/04/2020Chap. 9 Linear sound waves Project topic11/06/2020
32 Fri, 11/06/2020Chap. 9 Sound sources and scattering; Non linear effects
33 Mon, 11/09/2020Chap. 9 Non linear effects in sound waves and shocks #2111/11/2020
34 Wed, 11/11/2020Chap. 10 Surface waves in fluids #2211/16/2020
35 Fri, 11/13/2020Chap. 10 Surface waves in fluids; soliton solutions
36 Mon, 11/16/2020Chap. 11 Heat conduction
37 Wed, 11/18/2020Chap. 12 Viscous effects
38 Fri, 11/20/2020Chap. 13 Elasticity
39 Mon, 11/23/2020 Review
Wed, 11/25/2020 Thanksgiving Holiday
Fri, 11/27/2020 Thanksgiving Holiday
40 Mon, 11/30/2020 Review
Wed, 12/02/2020 Presentations I
Fri, 12/04/2020 Presentations II

PHY 711 -- Assignment #3

Aug. 31, 2020

Read Chapter 1 in Fetter & Walecka.

  • In Lecture 3, we derived equations relating the laboratory scattering angle to the scattering angle in the center of mass reference frame. We also worked out the relationship between the differential scattering cross sections in the laboratory and center of mass frames. After you have convinced yourselves of the validity of those derivations, evaluate both the lab and center of mass scattering angles and the corresponding cross section factors for the following mass ratios
    • m1/m2=1
    • m1/m2=1/10
    • m1/m2=10/1

PHY 711 -- Assignment #4

Sept. 4, 2020

Finish reading Chapter 1 in Fetter & Walecka.

  • Work Problem #1.16 at the end of Chapter 1 in Fetter and Walecka.

PHY 711 -- Assignment #5

Sept. 9, 2020

Start reading Chapter 3, especially Section 17, in Fetter & Walecka.

  • Using calculus of variations, find the equation y(x) of the shortest "curve" which passes through the points (x=0, y=0) and (x=5, y=8).
PHY 711 - Assignment #8
Sept. 16, 2020
Continue reading Chapters 3 and 6 in Fetter and Walecka.
PIC
  1. The figure above shows a box of mass m sliding on the frictionless surface of an inclined plane (angle θ). The inclined plane itself has a mass M and is supported on a horizontal frictionless surface. Write down the Lagrangian for this system in terms of the generalized coordinates X and s and the fixed constants of the system (θ, m, M, etc.) and solve for the equations of motion, assuming that the system is initially at rest. (Note that X and s represent components of vectors whose directions are related by the angle θ.)

PHY 711 -- Assignment #10

Sept. 23, 2020

Continue reading Chapters 3 and 6 in Fetter & Walecka.

PHY 711 -- Assignment #11

Sept. 28, 2020

Start reading Chapter 4 in Fetter & Walecka.

  1. Consider the the mass and spring system described by Eq. 24.1 and Fig. 24.1 in Fetter & Walecka. Explicitly consider the case of N=4 and find the 4 coupled equations of motion. Compare the normal mode eigenvalues for this case (obtained with the help of Maple or Mathematica) with the equivalent analysis given by Eq. 24.38.

PHY 711 -- Assignment #12

Sept. 30, 2020

Finish reading Chapter 4 in Fetter & Walecka.

  1. Consider the system of 3 masses (m1=m2=m3=m) shown attached by elastic forces in the right triangular configuration (with angles 45, 90, 45 deg) shown above with spring constants k and k'. Find the normal modes of small oscillations for this system. For numerical evaluation, you may assume that k=k'.

PHY 711 -- Assignment #14

Oct. 7, 2020

Continue reading Chapter 7 in Fetter & Walecka.

Consider the Sturm-Liouville equation (Eq. 40.9 in F & W) with τ=1, v(x)=0 and σ=1 for the interval 0 ≤ x ≤ 1 and the boundary values df(0)/dx=df(1)/dx=0.

  • Find the lowest eigenvalue and the corresponding eigenfunction.
  • Choose a reasonable trial function to estimate the lowest eigenvalue and compare the estimate to the exact answer.

PHY 711 -- Assignment #17

Oct. 23, 2020

Review Chapter 8 and Appendix E in Fetter & Walecka.