Convert angle of attack and sideslip angle to direction cosine matrix
The Direction Cosine Matrix Body to Wind block converts angle of attack and sideslip angle into a 3-by-3 direction cosine matrix (DCM). The DCM matrix performs the coordinate transformation of a vector in body axes (ox0, oy0, oz0) into a vector in wind axes (ox2, oy2, oz2). The order of the axis rotations required to bring this 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.
|2-by-1 vector||Contains the angle of attack and sideslip angle, in radians.|
|3-by-3 direction cosine matrix||Transforms body-fixed vectors to wind-fixed vectors.|
Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.