How did the Poisson brackets get derived, and from what.

[houlahound]

do they have a physical meaning and did they fall out of another theory.

I have only ever seen them stated as a fact, I am assuming they are a result of something ie a consequence of another more fundamental theory.

when are they used in a practical problem solving sense to solve real world problems?

 

[kreil]

http://en.wikipedia.org/wiki/Poisson_bracket