BRIEF SUMMARY: Classical mechanics
of systems of particles, and also continua such as fluids, including Lagrangian
mechanics, dynamics of systems of particles, non-inertial frames of reference,
chaotic oscillations, the Navier-Stokes equations of fluid motion, and
applications if continuum mechanics to diverse physical phenomena that may vary
from year to year. Examples
include: rotating fluids, waves,
vortices, flight, instabilities and turbulence.
The subject of classical mechanics is part of the core of physics. This course treats some of the traditional topics of classical mechanics at an intermediate level, but it also includes some topics of more recent interest, such as chaotic dynamics, that will help students to see mechanics as a lively subject that is still rapidly evolving. The second half of the course treats the dynamics of fluids, which is widely applicable to other disciplines including astrophysics, oceanography, the atmospheric sciences, engineering, and biological systems.
Mathematics and numerics: The following topics are probably familiar to some degree, and will appear at various points in the course: Vector cross product; line integrals; curl of a vector function; curvilinear coordinates; eigenvalues and eigenvectors of matrices; solving linear second-order differential equations with constant coefficients; numerical integration; and writing or modifying simple programs. I recommend Guide to Essential Math, by S. M. Binder and Boas - Mathematical Methods in The Physical Sciences as reference texts for the mathematics which occurs throughout undergraduate physics.
There will be two primary required texts:
Classical Mechaics by John R. Taylor: http://www.uscibooks.com/taylor2.htm
Physical Fluid Dynamics by D. J. Tritton, http://www.oup.com/us/catalog/he/subject/Engineering/MechanicalEngineering/FluidMechanics/?view=usa&ci=9780198544937
Other books on classical mechanics (on Reserve):
Fowles and Cassiday, “Analytical Mechanics”, 6th edition, 1999.
Barger and Olsson, Classical Mechanics: A Modern Perspective, 1995.
T.W.B. Kibble, Classical Mechanics (third edition, 1985). Written by a well known British theoretical physicist. It is available in paperback for a very modest price.
Baierlein, Newtonian Dynamics (1983). Less formal than Marion and Thornton; quite readable, but not as thorough.
P. Smith and R.C. Smith, Mechanics (1990). This modern book contains a treatment of chaotic dynamics, but the traditional material seems a bit dull.
Books on Chaos
G. Baker and J.P. Gollub, Chaotic Dynamics: An Introduction, second edition, 1996.
S. H. Strogatz, Nonlinear dynamics and chaos, 1994.
Other books on continuum mechanics
Physics of Continuous Matter, by B. Lautrup: http://www.nbi.dk/~lautrup/continuum/index.html
M. van Dyke, An Album of Fluid Motion
T.E. Faber, Fluid Dynamics for Physicists
E. Guyon et al., Physical Hydrodynamics
H.
Tennekes, The Simple Scioence of Flight
S. Vogel, Life in Moving Fluids
F.W. Taylor, Elementary Climate Physics
Regular attendance: You are expected to attend all classes and tutorials. Absences for any reason other than illness will be considered excessive if more than two in number at class or tutorial. If you are ill or expect to miss class due to special circumstances, a timely e-mail message to that effect is expected.
Preparation: You should come to class prepared. The best learning occurs when you read or skim the upcoming material before class, and then read more carefully after class. Interaction during lectures is expected and encouraged.
Homework: There will be regular homework
assignments. You are expected to
complete the homework (or at least to make a serious effort on each problem) on time.
Some problems will be designated as "individual" problems, for
which you may not consult with classmates, but may use the library.
Exams: There will be one take-home
midterm exam and a self scheduled final examination.
Exams (2) 30%, 30%
Homework 30%
Engagement and participation 10%
I will discard the two worst problem set grades before computing final grades.
Late assignments: Homework is due every wednesday in class, except on the week when the midterm exam is due. You may take one free extension during the semester.
Extensions: You may give yourself a "free extension" for up to one week without penalty once in the term. Please save it for a high pressure time. Simply turn in a sheet of paper with your name, the assignment number, and the remark that you are taking your "free extension." Finally, in case of illness you may request extra time, without using your free extension.
Absences after shopping period (for reasons other than illness) will be considered in the final evaluation if more than two were noted, generally by subtracting about 0.1 grade point per extra absence. (Three extra unexcused absences could reduce a grade from 4.0 to 3.7.)
You are allowed and encouraged to discuss homework with each other (except on "individual" problems), but it would be wise to attempt them yourself first. Your written work must be your own, though it may be influenced by prior discussion. This means, for example, that you may not look at another student’s written work while preparing your own.
Sources (e.g. books) or other assistance
should be acknowledged. However, you
don't need to acknowledge the help of students in your problem-solving group
since this interaction is understood.
The purpose of these provisions is to enhance your learning experience, and to enable the instructor to tell how well each student is doing.
This is an approximate list. I may adjust the content and rate depending on my perception of your learning.
Material from
Week 1 Momentum and angular momentum Ch. 1 and 3
Week 2 Energy Ch. 4
Week 3 Calculus of variations Ch. 6
Week 4 Lagrangian mechanics Ch. 7
Week 5 Lagrangian
mechanics
Ch. 7
Week 6 Central Force Problems
Ch 8
Break
Week 7 Mechanics in non-inertial frames Ch 9
Week 8 Hamiltonian mechanics Ch 13
Week 9 Hamiltonian mechanics Ch 13
Week 10 Pipe and channel flow Tritton Chapter 2
Week 11 The Navier stokes equations Tritton Chapter 5
Week 12 Streamlines, stream function, vorticity Tritton Chapter 6
Week 13 Exact solutions for viscous flow Tritton Chapter 9
Week 14 The turbulence problem Various readings