Unsolved Scientific Problems in Classical Mechanics

I have read that complicated fluid dynamics and turbulence is still a beast to deal with.
e.g. http://www.livescience.com/33075-how-bees-fly.html -- scientists took a while to figure out how bumble bees generate enough lift for flight.

 

For classical mechanics, the N-body problem is still unsolved, except for a few special cases. It's been around since Newton.

http://en.wikipedia.org/wiki/N-body_problem

 

Not sure if important, but I think there is still missing A classical mechanics-only approach to geometric phases in chaotic systems .