I'm making a game which you can see here, if you are on Windows or Linux: http://insertnamehere.org/birdsofprey/
If you click and hold your mouse on a bird, you can see I'm just swinging the bird back and forth in pendulum motion. I would like to, instead, implement a more realistic motion, where the movement of your mouse affects the swinging of the bird like a pendulum with a moving pivot.
I found a document on this topic but the equations rely on knowing the pivot's acceleration (X'' and Y''), which I do not; I am only repeatedly translating the bird graphic to the current mouse position.
I have the bird's angle (-180 to 180 degrees), angular velocity and acceleration. I will need to alter these three variables each time the mouse is moved, so I will also have the last (x,y) and the new mouse (x,y).
Is this enough to make a good simulation of a pendulum with moving pivot?