I'm trying to solve a problem to do with forces as represented by this freebody diagram.

The large circle represents a body, that is free to rotate about axis A, that has a complex of external, non-contact forces acting upon it represented by the wiggly red arrows. The composite of these forces is calculated (by a library call using Stress Tensor integration), and the combined result is returned as (ex.) X: 335.123 N Y: -74.2858 N.

In addition to the body being free to rotate about A, the short (10 units) link arm it is attached to can rotate about the axis B.

The problem is to work out what position the combined mechanism will end up in as a result of the forces acting upon it.

For now, I'm ignoring the possibility that forces acting may change as the assembly rotates. This is part of a complex simulation and the basic idea is that from a known starting point, I use the library to calculate the net force acting at some instance in time; from that work out the position the assembly moves to; adjust the model to reflect that movement, and then re-calculate the stress tensor integration for the next instance. If the time-step is small enough and the iteration count high enough, then it should give a reasonable approximation of the affects of the forces over time.

In keeping with the "what have you got so far" ethic, the second (lower) state diagram in the image shows what I think will happen.

• The short link A-B will rotate anticlockwise about B by an angle (to the horizontal) represented by the purple line that connects B to a point F, which is a point on the periphery of the circle through which the resultant of the X/Y force acts through A in the original position.
• The body will rotate clockwise around A such that the position of the point F on its periphery will end up in the same place(ish) as it was in before the movement takes place.

I realise that the position of F in the resultant is slight displaced from its original position in space, but as shown, the angles involved are greatly exaggerated. The actual actual angles will be very small at each iteration, so the inaccuracy at each step will also be small. In the end, it is the position of the body in space that is important, not its rotation, nor the exact position of any point on it.

I'm fairly sure I can handle coding the trig to resolve the two rotations; what I'm looking for here is any kind of argument for or against my assessment of what will happen?

My thanks to anyone with enough math to tackle the problem and bored enough to bother :)