PHY 337/637 Analytical mechanics

PHY 337/637 Analytical Mechanics

TR 12:30 -1:45 PM

OPL 103

http://www.wfu.edu/~natalie/f23phy337/

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

Course schedule

In the table below, Reading refers to the chapters in the Cline textbook , PP refers to textbook section listing practice problems to be discussed at the course tutorials, and Assign is a link to the graded homework for the lecture. The graded homeworks are due each Tuesday following the associated lecture. (Preliminary schedule -- subject to frequent adjustment.)

	Date	Reading	Topic	PP	Assign
1	Tu, 8/29/2023	Ch. 1 & 2	Introduction, history, and motivation	2E	#1
2	Th, 8/31/2023	Ch. 5	Introduction to Calculus of variation	5E	#2
3	Tu, 9/05/2023	Ch. 5	More examples of the calculus of variation	5E	#3
4	Th, 9/07/2023	Ch. 6	Lagrangian mechanics	6E	#4
5	Tu, 9/12/2023	Ch. 7 & 8	Hamiltonian mechanics	8E	#5
6	Th, 9/14/2023	Ch. 7 & 8	Hamiltonian mechanics	8E
7	Tu, 9/19/2023	Ch. 13	Dynamics of rigid bodies	13E	#6
8	Th, 9/21/2023	Ch. 13	Dynamics of rigid bodies	13E	#7
9	Tu, 9/26/2023	Ch. 13 & 11	Review of rigid bodies and intro to scattering	11E	#8
10	Th, 9/28/2023	Ch. 11	Scattering theory	11E	#9
11	Tu, 10/3/2023	Ch. 11	Scattering theory	11E
12	Th, 10/5/2023		Summary and examples		Take home exam start
13	Tu, 10/10/2023		Comments on more modern uses of analytical mechanics		Take home exam due
	Th, 10/12/2023	Fall Break
14	Tu, 10/17/2023		Course summary

PHY 337/637 -- Assignment #2

Assigned: 8/31/2023 Due: 9/5/2023

Start reading Chapter 5 in Cline.

Using calculus of variations, find the equation, y(x), of the shortest length "curve" which passes through the points (x=0, y=0) and (x=3, y=4). What is the length of this "curve"?

PHY 711 -- Assignment #4

Assigned: 9/07/2023 Due: 9/12/2023

Continue reading Chapter 6, in Cline.

Consider a point particle of mass m moving (only) along the x axis according to a force F_x=-K x, where K is a positive constant. The particle trajectory as a function of time, x(t), has the initial value x(t=0)=C, where C denotes a given length, and its initial velocity is 0.

Write down and solve Newton's second law for this system, finding the form of the trajectory x(t).
Now write down the Lagrangian for this system and solve the Euler-Lagrange equations for the trajectory x(t). How does your answer compare with (a)?

PHY 711 -- Assignment #6

Assigned: 9/19/2023 Due: 9/26/2023

Read Chapter 13 in Cline.

The figure shows a system with 4 masses held rigidly at the given locations with massless supports similar to the example in lecture.

Evaluate the moment of inertia tensor for this system.
Find the principal moments of inertia.
Find the corresponding principal axes.

PHY 711 -- Assignment #7

Assigned: 9/21/2023 Due: 9/26/2023

This is an opportunity to re-examine HW 5 and earn more points for your corrected solution (up to 90 percent of the 2 point total).

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Last modfied: Monday, 09-Oct-2023 17:12:05 EDT