Direction Cosine Matrix Body to Wind
Convert angle of attack and sideslip angle to direction cosine matrix
Aerospace Blockset / Utilities / Axes Transformations
The Direction Cosine Matrix Body to Wind block converts angle of attack and sideslip angles into a 3-by-3 direction cosine matrix (DCM). This direction cosine matrix is helpful for vector body axes to wind axes coordinate transformations. To transform the coordinates of a vector in body axes (ox0, oy0, oz0) to a vector in wind axes (ox2, oy2, oz2), multiply the block output direction cosine matrix with a vector in body axes. For information on the axis rotations for this transformation, see Algorithms.
ɑ β — Angle of attack and sideslip angle
Angle of attack and sideslip angle, specified as a 2-by-1 vector, in radians.
DCMwb — Direction cosine matrix
3-by-3 direction cosine matrix
Direction cosine matrix, returned as 3-by-3 direction cosine matrix.
The order of the axis rotations required to bring this transformation about is:
A rotation about oy0 through the angle of attack (α) to axes (ox1, oy1, oz1)
A rotation about oz1 through the sideslip angle (β) to axes (ox2, oy2, oz2)
Combining the two axis transformation matrices defines the following DCM.
 Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation. Hoboken, NJ: John Wiley & Sons, 1992.