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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