Whilst not exactly related to your question, I suggest you have a look at "pilot induced oscillations". Some interesting video too. I expect Sully was ensuring he avoided it.
I hadn't heard of this accident, but it's PIO and autopilot related. http://skybrary.aero/bookshelf/books/681.pdf In this instance the effects of not having the seat belt on at all times was fatal for 50% of the passengers. And yet the aircraft survived to fly again.
