Convert wind angles to direction cosine matrix
Aerospace Blockset / Utilities / Axes Transformations
The Wind Angles to Direction Cosine Matrix block converts three wind rotation angles into a 3-by-3 direction cosine matrix (DCM). The DCM matrix performs the coordinate transformation of a vector in earth axes (ox0, oy0, oz0) into a vector in wind axes (ox3, oy3, oz3). For more information on the direction cosine matrix, see Algorithms.
This implementation generates a flight path angle that lies between ±90 degrees, and bank and heading angles that lie between ±180 degrees.
μ γ χ— Wind rotation angles
Wind rotation angles, specified as a 3-by-1 vector, in radians.
DCMwe— Direction cosine matrix
Direction cosine matrix, returned as a 3-by-3 matrix.
The DCM matrix performs the coordinate transformation of a vector in earth axes (ox0, oy0, oz0) into a vector in wind axes (ox3, oy3, oz3). The order of the axis rotations required to bring this about is:
A rotation about oz0 through the heading angle (χ) to axes (ox1, oy1, oz1)
A rotation about oy1 through the flight path angle (γ) to axes (ox2, oy2, oz2)
A rotation about ox2 through the bank angle (μ) to axes (ox3, oy3, oz3)
Combining the three axis transformation matrices defines the following DCM: