Direction Cosine Matrix Body to Wind

Convert angle of attack and sideslip angle to direction cosine matrix


Utilities/Axes Transformations


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:

  1. A rotation about oy0 through the angle of attack (α) to axes (ox1, oy1, oz1)

  2. A rotation about oz1 through the sideslip angle (β) to axes (ox2, oy2, oz2)


Combining the two axis transformation matrices defines the following DCM.


Dialog Box

Inputs and Outputs

InputDimension TypeDescription


2-by-1 vectorContains the angle of attack and sideslip angle, in radians.

OutputDimension TypeDescription


3-by-3 direction cosine matrixTransforms body-fixed vectors to wind-fixed vectors.


Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.

Introduced before R2006a

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