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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)

Combining the three axis transformation matrices defines the following DCM.

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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