PHY 401, Fall '04
Intermediate Mechanics


Instructor: Finn Larsen

 
 
LECTURES
Mon+Wed+Fri 9-10 am; 501 Dennison.
TEXTBOOK
Thornton and Marion, Classical Dynamics of Particles and Systems,
5th edition. Thomson (2004)

SECTIONS
Thu 6.30-9.30pm; Randall 2246
Beth Percha, perchab@umich.edu

GRADER
Yanou Cui, yocui@umich.edu
OFFICE HOURS
Tue+Thu 2-3 pm; or by appointment.
CONTACT INFO
Office: Randall 3464; e-mail: larsenf@umich.edu; phone: 763-4325




COURSE DESCRIPTION



This is a one semester course on analytical mechanics, the rigorous and mathematical
treatment of classical mechanics.
We will introduce powerful physical concepts such as
symmetry, Lagrangians, and phase space; and apply mathematical tools like linear
algebra, vector calculus, and differential equations. These methods provide foundations
for the study of quantum mechanics and modern physics.
Mechanics is therefore a
central course in the physics curriculum.


Some of the important physics concepts that will be covered are:
1) Symmetry and conservation laws
2) Small oscillations and normal coordinates
3) Central forces and scattering
4) Rigid body motion
5) Lagrangian and Hamiltonian dynamics



SYLLABUS

 
The following is a TENTATIVE schedule. The material to be covered may change slightly, depending on progress.

Week
Monday Lecture
Wednesday Lecture
Friday Lecture
Sep 6-10
LABOR DAY
Intro: Scalars and Vectors (1.1-3,11)
Matrices (1.4-10,12)
Sep 13-17
Multivariable Calculus (1.13-14,16-17)
Newton's Laws (2.1-3)
Single Particle Motion (2.4, -p71)
Sep 20-24
Conservation Laws (2.5)
Energy (2.6-2.7)
Harmonic Oscillations (3.1-3)
Sep27-Oct1
Phase Space and Damped Oscillations (3.4-5)
Driven Harmonic Oscillators (3.6-7)
Principle of Superposition (3.8)
Oct 4-8
Gravitation (5.1-5.4)
Tidal Forces (5.5) Midterm #1 (Chs 1-3, 5)
Oct 11-15
Calculus of Variations (6.1-3) Constraints and Lagrange Multipliers (6.5-7) Hamilton's Principle and the Lagrangian (7.1-2)
Oct 18-22
FALL BREAK
Generalized Coordinates (7.3-4) Equivalence with Newton's equations (7.5-7)
Oct 25-29 
Symetry and Conservation Laws (7.8-9) Hamiltonian Dynamics (7.10-11) Central Force Motion (8.1-6)
Nov 1-5
Kepler's Laws (8.7-8) Systems of Particles (9.1-5) Elastic Collistions (9.6)
Nov 8-12
Kinematics of Scattering (9.7-8) Scattering Cross-section (9.9-9.10)
Midterm #2 (Chs. 6-9)
Nov 15-19 Non-inertial Reference Frames (10.1-3) Motion Relative to the Earth (10.4) The Moment of Inertia Tensor (11.1-3)
Nov 22-26
Angular Momentum (11.4-5) More on Moments of Inertia (11.6-7) THANKSGIVING
Nov29-Dec3
Euler Angles and Euler Equations (11.8-9) Force-Free Motion (11.10+11) Small Oscillations (12.1-3)
Dec 6-10
Coupled Oscillators and Normal Coordinates (12.4,6) Molecular Vibrations (12.7) The Loaded String (12.9)
Dec 13-17
Epilogue
READING PERIOD 
READING PERIOD

 


HOMEWORK


Homework is DUE EACH FRIDAY AT 9AM.
Solutions will generally be posted shortly
after that time so
it will NOT be possible to receive extensions. Assignments must be written
legibly on stapled pages to receive credit. You are welcome to study and work on homework
together. However, you must personally write out and turn in your problem set.

The Homework problems below refer to the textbook.
Note that the assignments could
change slightly to adjust for changes in schedule (Check back on this page).


HW#
Due Date
Problems
Solutions
1
Sep 17
1.1, 1.8, 1.10, 1.13, 1.14, 1.27, 1.31
SOL1.pdf
2
Sep 24
2.4, 2.17, 2.27, 2.29, 2.34a,2.37  SOL2.pdf
3
Oct 1
2.52, 3.1, 3.10, 3.12, 3.22 SOL3.pdf
4
Oct 8
3.18, 3.28, 5.4, 5.14, 5.15 SOL4.pdf
5
Oct 15
6.2, 6.7, 6.12, 6.15 SOL5.pdf
6
Oct 22
7.4, 7.5, 7.7, 7.14, 7.21 (skip phasediagram) SOL6.pdf
7
Oct 29
7.22, 7.30, 7.34, 7.38 SOL7.pdf  
8
Nov 5  
8.5, 8.11, 8.25, 9.2, 9.13 SOL8.pdf 
9
Nov 12
9.23, 9.35, 9. 38, 9.43 SOL9.pdf  
10
Nov 19
9. 46, 10.3, 10.6, 10.12, 10.22 SOL10.pdf
11
Dec 3
11.1, 11.6, 11.11, 11.12, 11.17, 11.27 SOL11.pdf
12
Dec 10
12.1, 12.2, 12.16, 12.23, 12.26 SOL12.pdf




EVALUATION


There will be 2 midterms (dates are indicated on the syllabus) and one final
(scheduled
for Monday Dec 20, 1.30-3.30pm
). The GRADE will be determined from:
1) HOMEWORK  20%.
2) MIDTERMS 20% each
.
3) FINAL 40%.




OTHER TEXTBOOKS



There are numerous textbooks on mechanics. Each has slightly different emphasis and
people have different preferences. I have requested that the following be placed on reserve
at the science library:

1) Marion and Thornton, Classical Dynamics of Particles and Fields.  
This is the textbook for this course. Although not universally praised, to put it
diplomatically, it is the best one available: it has the right level and covers the material
needed for further studies.
This is probably the most popular book used for this type
of course at
universities comparable to UM.

2) K. R. Symon, Mechanics.
A good alternative textbook at the same level at MT. The weakness is that some parts of
the book is old-fashioned.

3) V. Barger and M. Olsson, Classical Mechanics: A Modern Perspective.
Another textbook with a modern perspective. Apparently less thorough (reports indicate
lack of examples and frequent errors).

4) R. P. Feynman, The Feynman Lectures on Physics.
Classic lectures by a master physicist. Great for intuition and innovative examples, but
short on systematic development of formalism.

5) H. Goldstein, Classical Mechanics.
Graduate level. The standard, authoritative reference.

6) Landau and Lifshitz, Mechanics.

Graduate Level. Straight to the point and insightful; but somewhat terse.