Download Bill,I think this is an excellent topic

Bill,
I think this is an excellent topic. It is not only that Hamiltonian
dynamics is first order but also one can explicitly conserve energy in
the dynamics. The buzzword is "symplectic integrator". An
introduction and some references are in wikipedia:
http://en.wikipedia.org/wiki/Symplectic_integrator
Have a look at this and some references and we should then talk more
specifically about what you want to cover. If no one had chosen this
topic I was going to say something about it in class. Your report
could either include an introduction (in which case I would not
discuss it in class except in passing and to advertise your report) or
you could assume I will introduce the topic theoretically and you will
do something more applied/specialized.
Sincerely,
Prof. Machta
On Sat, Oct 30, 2010 at 4:24 PM, William Barnes
<[email protected]> wrote:
[Hide Quoted Text]
Hello Prof. Machta,
I'm considering my approach to the final project, and am 99% sure that I
will do something along the lines of computation / simulation. I have a
strong background in programming, and have had lots of fun and success in
simulating all sorts of classical physics scenarios.
I'd like to expand my horizon and try to build off of a comment you made in
class about Hamiltonian dynamics. Specifically, I remember hearing that
numerically simulating physical systems using Hamiltonian dynamics is
advantageous because the equations are of first order.
My rough idea is to find a number of problems that may or may not have an
analytic solution. Then, I hope to find solutions using old tried-and-true
computation techniques: Newton's method, Euler's method, Runge-Kutta, etc.
Immediately following I hope to demonstrate that the same analysis using
Hamiltonian dynamics is somehow better. (Faster convergence, or simultaneous
solutions, or whatever..)
Before I jump into the journals and literature, it might be worth having
your opinion of this topic for a final project. Also, can you point out any
specific things I might want to be aware of? Maybe there is a problem out
there already that showcases the advantage of numerical Hamiltonian
dynamics?
Thanks very much, and Happy Halloween!
BBarnes