Dear Masoud,
FAST uses a nonlinear form of the rotation matrix you’ve stated. The rotation matrix depends on the flapwise and edgewise mode shapes, the displacements of the blade DOFs, and the structural twist angle. The exact matrix is described in the “Unofficial FAST Theory Manual” mentioned in the following forum topic: Coupled blade modes in FAST. I believe I’ve already sent this to you by e-mail.
The mode shapes are specified in FAST in the blade coordinate system (xb/yb/zb).
Best regards,