**Physics 410**

*Advanced Mechanics*

**Fall Term, 2006**

**1:50 – 3:00 MWF,
Youngchild Hall Room 115**

**Professor Matthew Stoneking**

**Catalog course description:
**Treats various topics
selected from: mechanics of rigid bodies, Lagrangian and Hamiltonian formulations,
variational principles, fluids, classical scattering, relativistic mechanics,
and theory of small vibrations.

*Text:*** Classical Dynamics of Particles and
Systems**, 5^{th} Edition, by Stephen T. Thornton
and Jerry B. Marion, (Thomson Brooks/Cole Publishing, 2004).

*Other
mechanics texts on reserve in the library:*

**Mechanics**, by Keith R. Symon

**Classical
Mechanics**, by Herbert
Goldstein

**An
Introduction to Mechanics**,
by Daniel Kleppner and Robert J. Kolenkow

**Classical
Mechanics, a Modern Perspective**,
by

**Classical
Mechanics**, by A. Douglas
Davis (*not on reserve*)

*Office hours: *Wednesday 9:30
– 11:00 AM, Thursday 1:30 – 3:00 PM. Appointments
can also be made to meet with instructor.

*Grading policy:*

Grades will be
assigned based on the following elements, weighted as indicated:

·
Midterm
Exam: 20%

·
Final
Exam: 25%

·
Problem
sets: 30%

·
Problem
Presentations: 15%

·
Attendance
/ Participation: 10%

*Exams:*

The midterm exam will be a take home
exam. The final exam will be cumulative
and will take place during the regularly scheduled final exam time (Friday, 8
December, 1:30 PM).

*Problem sets:*

Problem sets will be assigned almost
every week (probably ~8 total), and will usually be due in class on Friday of
each week. Students are encouraged to
collaborate on problem solutions, but each student must submit his own write-up
of solutions and each student must participate in the solution of each problem.

Problem Set #1 (due: Fri. 9/29): T&M,
Chap. 7, problems 3, 6, 7, 9, 10, 14, 15, 21

Problem Set #2 (due: Mon. 10/9): T&M,
Chap. 7, problems 11, 20*, 23, 24, 28, 30*, 31*, 37*

Problem Set #3 (due: Wed. 10/18):
T&M, Chap. 10, problems 8*, 9*, 15*, 19, 22*

Problem Set #4 (due: Fri. 11/3): T&M,
Chap. 12, problems 1*, 2, 7*, 8*, 11, 13*, 17, 26, 28

Problem Set #5 (due: Mon. 11/13):
T&M, Chap. 13, problems 8, 14, 17, 18, 19, 22

Problem Set #6 (due: Fri. 12/1): David,
Chap. 12, problems 10, 12*, 13*, 16*, 18*, 19

*problems presented in class

*Problem Presentations:*

Each student will make three problem
solution presentations in class. Grades
will be based on the effectiveness of the presentation style as well as the
quality and completeness of the solution.
Presentations should therefore be rehearsed and solutions should be
checked by the instructor prior to class.

*Outline of Topics
Covered:*

I.
Lagrangian and Hamiltonian Dynamics (T&M
chapters 6 and 7)

II.
Motion in Noninertial Reference Frames (M&T
chapter 10)

III.
Dynamics of Rigid Bodies (M&T chapter 11)

IV.
Coupled Oscillations (M&T chapter 12)

V.
Vibrating Systems and the Wave Equation (M&T
chapters 13)

VI.
Fluid Mechanics (supplemental reading)

VII.
Special Relativity (M&T chapter 14)

*Schedule: *The following is a tentative schedule of
topics to be covered in this course.

1.
Wed. 20 September

Review of Newtonian mechanics and
derivation of Lagrange’s Equations from ^{nd} Law (see sections 7.6, 7.7)

2.
Fri. 22 September

Example problems using Lagrange’s
Equations,

Read T&M Chapter 6 and Chapter 7
(sections 7.1 – 7.4)

3
Mon. 25 September

Generalized momenta, ignorable
coordinates and constants of the motion,

Velocity-dependent potential energy and
the Lagrangian for a charged particle in an electromagnetic field

Read T&M, Chapter 7 (sections 7.6 –
7.9)

4.
Wed. 27 September

Lagrange Undetermined Multipliers and
Constraint Forces

Read T&M Chapter 7 (section 7.5 )

5.
Fri. 29 September

Hamiltonian dynamics and the Virial
Theorem

Read T&M Chapter 7 (sections 7.10 -
7.13)

Problem set #1 due

6.
Mon. 2 October

Noninertial reference frames and
fictitious forces

Read T&M Chapter 10 (sections 10.1 –
10.3)

7.
Wed. 4 October

Problems involving centrifugal and
Coriolis forces

Read T&M Chapter 10 (section 10.4)

8.
Fri. 6 October

Problem session on Lagrangian and
Hamiltonian dynamics

9.
Mon. 9 October

Coriolis force and the Larmor Theorem in
electrodynamics

Rigid body rotational dynamics: angular
momentum and the inertia tensor

Read T&M Chapter 11 (sections 11.1 –
11.4)

Problem Set #2 due

10.
Wed. 11 October

Rotational kinetic energy, principal
axes, the parallel-axis theorem, and Euler’s equations

Read T&M Chapter 11 (sections 11.5 –
11.7, 11.9)

11.
Fri. 13 October

Stability of rotations about principal
axes (the tennis racket theorem)

Read T&M Chapter 11 (section11.12)

12.
Mon. 16 October

The Force-free (torque-free) symmetric
top, Euler angles

Read T&M Chapter 11 (sections11.8,
11.10)

13.
Wed. 18 October

Problem session on noninertial reference
frames

Problem Set #3 due

14.
Fri. 20 October

Euler angles and the symmetric top with
one point fixed

Read T&M Chapter 11 (section 11.8,
11.11)

Midterm exam handed out

15.
Mon. 23 October

Two coupled harmonic oscillators, normal
modes

Read T&M Chapter 12 (sections 12.1 –
12.3, 12.6 – 12.8)

16.
Wed. 25 October

The Loaded String

Read T&M Chapter 12 (section 12.9)

Fri. 27 October Midterm Reading Period … no
class

Midterm Exam Due

17.
Mon. 30 October

This class session will be rescheduled
because the instructor will be out of town at a physics conference.

18.
Wed. 1 November

Problem session on coupled oscillations

There will be a substitute instructor for
this class session because the instructor will be out of town at a physics
conference.

19.
Fri. 3 November

Waves on a string under tension. The classical wave equation. Phase velocity. Fourier analysis.

Read T&M Chapter 13 (sections 1-4,
6-8)

Problem set #4 due

20.
Mon. 6 November

Wave packets and group velocity. Fluid
statics

Read T&M Chapter 13 (section 9)

21.
Wed. 8 November

Fluid statics, the continuity equation.

Read Davis Chapter 12 (sections 1-2)

22.
Fri. 10 November

Fluid momentum equation, Bernoulli’s
theorem.

Read David Chapter 12 (sections 3-4)

23.
Mon. 13 November

Applications of Bernoulli’s equations,
sound waves in a gas.

24.
Wed. 15 November

Fourier transforming differential
equations, sound waves and electromagnetic waves revisited, plasma waves.

Problem Set #5 due

25.
Fri. 17 November

Water waves. Viscosity.
The Navier-Stokes equation.

26.
Mon. 20 November

Poiseuille flow (viscous flow through a
cylindrical pipe).

Special relativity: the postulates and the
Lorentz transformation equations, velocity addition

Read T&M Chapter 14 (sections 14.1 –
14.4)

Thanksgiving
Break

27.
Mon. 27 November

Invariant spacetime interval, spacetime
diagrams, time dilation and length contraction, line-of-sight Doppler effect

Read T&M Chapter 14 (sections 14.5)

17.
Tues. 28 November (makeup class)

Doppler effect for general orientation and
relative motion of source and receiver. Four-vectors. Relativistic momentum and energy.

Read T&M Chapter 14 (sections 14.7 - 14.9)

28.
Wed. 29 November

Problem session on fluids

29.
Fri. 1 December

Understanding the Twin Paradox using
spacetime diagrams. Examples using
relativistic energy and momentum conservation.

Read T&M Chapter 14 (sections 14.6, 14.10
– 14.11)

Problem set #6 due

*FINAL EXAM: Friday 8
December 1:30 PM*