“…
it was not clear to me as a young student that access to a more profound
knowledge of the more basic principles of physics depends on the most intricate
mathematical methods. This dawned
on me only gradually after years of independent scientific work."
---
Albert Einstein
Tips on making effective presentations
Chaos
in the solar system
Lynx and hare
populations in Canada
The
falling chain
Earth's
J2 is changing!
OLD NEWS
WELCOME!
Text:
Classical Dynamics of Particles
and Fields, 4th edition, by Marion and Thornton.
See the syllabus for more detailed information.
This is the first semester in which you really apply the mathematics you have learned, and in which really begin to discover some of the more sophisticated concepts in physics. Your first taste of this was in PS 303 - Modern Physics, and now your "physical education" begins in earnest.
We will cover:
Fundamentals of mechanics, oscillatory
motion, systems of particles, varying mass, motion under central forces,
motion in three dimensions, gyroscopic motion, generalized coordinates,
normal coordinates, Lagrangian and Hamiltonian formulations, and numerical
projects.
Prerequisites: MA 345 (Differential Equations
and Matrix Methods), ES 204 (Dynamics), PS 219 (Physics III).
Corequisites: PS 303 (Modern Physics)
SCHEDULE
|
Week |
Topics |
Chapters
in Marion |
|
1-4 |
Newton’s
laws |
1, 2 |
|
5-9 |
Linear
oscillations |
3 |
|
10-13 |
Central
force motion |
8 |
|
14 |
Project presentations |
|
For a short overview of chaos, read the FAQ from sci.nonlinear.
Some links to nonlinear dynamics and chaos are listed here to give you some starting ideas for your project. I have several good books in my office that you can check out for other ideas.
Useful books in the LIBRARY:
Understanding Nonlinear Dynamics, by Kaplan
& Glass, QA 845.K36 1995
Chaotic Vibrations: An Introduction for Applied Scientists and Engineers,
by Moon, QA 845.M66 1987
Introduction to Experimental Nonlinear Dynamics, by Virgin, QA 845.V57
2000
Order within Chaos, by Berge, Pomeau & Vidal, QA 614.8 B4713 1986
Nonlinear Oscillations, by Nayfeh & Mook, QA 402 N34 1979
Nonlinear Oscillations in Physical Systems, by Hayashi, QA 867.5 H39 1985
Exploring Chaos, by Hall, Q172.5.C45 E98 1993
Useful
web sites:
Nonlinear
math archive
Chaos
at Maryland
Nonlinear
Glossary
newsgroup:
sci.nonlinear
If you absolutely have no ideas, choose one of the following systems to analyze
I
- The van der Pol oscillator
van
der Pol 1
van
der Pol 2
van
der Pol 3
II - The Duffing attractor
Duffing
1
Duffing
2
Duffing
3
III - The Lorenz attractor
Lorenz
1
Lorenz
2
Lorenz
3
Matlab example. Here are the two files that we
discussed in class that solves the Volterra system:
volterra.m
fvol.m
If you still have no ideas, here are some possibilities
the restricted 3 body problem (i.e., chaos in the solar system)
Chua's oscillator
population models (e.g., the spread of diseases)
nonlinear electrical circuits
chemical reaction dynamics (e.g., the B-Z reaction)
synchronous
firefly flashing
neuron firing
chaotic pendulums
chaotic heartbeats
the spring pendulum
coupled oscillators
nonlinear springs
Vito
Volterra (1860-1940), mathematician interested in integral equations
and predator-prey models.
Info concerning the Lotka-Volterra
model. Some other models of populations can be found here
and here.
Jocopo Riccati, physicist and mathematician who worked on nonlinear differential equations.
Jacob Bernoulli (1645-1705), first of the great Bernoulli family to study mathematics and astronomy.
Robert
Carpick, contemporary physicist who researches tribology, the study of
friction.
On reserve
at the Jack R. Hunt Library are the following items:
Lectures on Physics,
by Richard Feynman - a Nobel Prize winner deeply explains the why of physics.
Mechanics,
by Keith Symon - another text at about the same level as Marion.
Classical Mechanics,
by Herbert Goldstein - a graduate-level text for those who wish more detail.
(The following items are on reserve for
my PS 103 course. They can be, however, useful for you if you feel
that you need some review. Do not hesitate to read through them,
if only to realize how far you have come in two years!)
Understanding
Physics, by Isaac Asimov - a great science fiction writer explains
physics.
Cartoon Guide
to Physics, by Huffman - physical principles in a visual format.
Practice at problem solving is an important
part of learning physics. I suggest that
you work as many problems as possible. I will post solutions
to most of the assigned homework problems.
http://www.indiana.edu/~wts/wts/plagiarism.html
http://www.rbs2.com/plag.htm
http://www.rbs0.com/tw.htm
http://www.rbs0.com/tw2.htm
(There are lots of links on this site)
