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# Direction Cosine Matrix to Wind Angles

Convert direction cosine matrix to wind angles

## Library

Utilities/Axes Transformations

## Description

The Direction Cosine Matrix to Wind Angles block converts a 3-by-3 direction cosine matrix (DCM) into three wind rotation angles. 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.

To determine wind angles from the DCM, the following equations are used:

## Inputs and Outputs

InputDimension TypeDescription

First

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

OutputDimension TypeDescription

First

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

## 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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