Wind Angles to Direction Cosine Matrix

Convert wind angles to direction cosine matrix

Library

Utilities/Axes Transformations

Description

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). The order of the axis rotations required to bring this about is:

  1. A rotation about oz0 through the heading angle (χ) to axes (ox1, oy1, oz1)

  2. A rotation about oy1 through the flight path angle (γ) to axes (ox2, oy2, oz2)

  3. A rotation about ox2 through the bank angle (μ) to axes (ox3, oy3, oz3)

[ox3oy3oz3]=DCMwe[ox0oy0oz0][ox3oy3oz3]=[1000cosμsinμ0sinμcosμ][cosγ0sinγ010sinγ0cosγ][cosχsinχ0sinχcosχ0001][ox0oy0oz0]

Combining the three axis transformation matrices defines the following DCM.

DCMwe=[cosγcosχcosγsinχsinγ(sinμsinγcosχcosμsinχ)(sinμsinγsinχ+cosμcosχ)sinμcosγ(cosμsinγcosχ+sinμsinχ)(cosμsinγsinχsinμcosχcosμcosγ]

Dialog Box

Inputs and Outputs

InputDimension TypeDescription

First

3-by-1 vectorContains wind angles, in radians.

OutputDimension TypeDescription

First

3-by-3 direction cosine matrixTransforms earth vectors to wind vectors.

Assumptions and Limitations

This implementation generates a flight path angle that lies between ±90 degrees, and bank and heading angles that lie between ±180 degrees.

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