Read up a little on "Flex" feature. That is one way to do it. It really depends on what you mean by "dynamically". Are you after closing a door in an assembly? Or something more design intensive?
Do you need to be able to animate the open and close? If not, you could model the hinge as a sheet metal part with a bend in it. Then you can flatten it (ie "open it") and everything should move correctly.
What you could do is model the lid twice. Once in the open position. And secondly in the closed position. Create a configuration that would allow you to toggle between the two.
Hope this helps.
Retrieving data ...