Direction Cosine Matrix Body to Wind

Convert angle of attack and sideslip angle to direction cosine matrix

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  • Aerospace Blockset / Utilities / Axes Transformations

Description

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.

Ports

Input

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Angle of attack and sideslip angle, specified as a 2-by-1 vector, in radians.

Data Types: double

Output

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Direction cosine matrix, returned as 3-by-3 direction cosine matrix.

Data Types: double

Algorithms

The order of the axis rotations required to bring this transformation 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)

[ox2oy2oz2]=DCMwb[ox0oy0oz0][ox2oy2oz2]=[cosβsinβ0sinβcosβ0001][cosα0sinα010sinα0cosα][ox0oy0oz0]

Combining the two axis transformation matrices defines the following DCM.

DCMwb=[cosαcosβsinβsinαcosβcosαsinβcosβsinαsinβsinα0cosα]

References

[1] Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation. Hoboken, NJ: John Wiley & Sons, 1992.

Introduced before R2006a