Ohhh boyy this one was a doozy. 4 years and almost 2 degrees later I can finally answer this question. I'm reviving this ancient thread because it is the first example in google when you search "simple symplectic reduction", and also there are very few examples of applied symplectic reduction...
Here's a link to a paper that I'm more or less trying to follow:
http://www.utdallas.edu/~txo140730/papers/SymRedOptCtrl.pdf
Example 5.2 from that paper is precisely what I'm trying to do, although probably through a different method. I'd be happy with either one. They begin with a system of 10...
Homework Statement
I'm struggling to perform a symplectic reduction and don't really understand the process in general. I have a fairly solid understanding of differential equations but am just starting to explore differential geometry. Hopefully somebody will be able to walk me through this...