https://github.com/d3x0r/STFRPhysics/blob/master/Development.md (The Long story)

My rotation vector equation/function for rotating the vector was curve fitted to intrinsic rotations, that is for a frame, picking some direction within that frame, then using that axis of rotation to spin the frame relative to that; while matrix multiplication and quaternion multiplication are extrinsic multiplications, which are applied outside of the frame.

I think that the overall order of operations also gets inverted; that for a multi-part ragdoll body, moving the body itself in my system updates the body, which then multiplies outward on each subsequent joint, using each composite to multiply out to the ends.

I think maybe quaternions and matrices are often applied in the other direction? From the leaves of a graph to the trunk? (I think in reality there's usually changes in all joints, so caching partial results doesn't matter a lot; but in the latter case, if the limbs don't move, then they only have to be multiplied by the core again when the body updates ?