# Documentation

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# dcm2alphabeta

Convert direction cosine matrix to angle of attack and sideslip angle

## Syntax

`[a b] = dcm2alphabeta(n)`

## Description

`[a b] = dcm2alphabeta(n)` calculates the angle of attack and sideslip angle, `a` and `b`, for a given direction cosine matrix, `n`. `n` is a 3-by-3-by-`m` matrix containing `m` orthogonal direction cosine matrices. `a` is an `m` array of angles of attack. `b` is an `m` array of sideslip angles. `n` performs the coordinate transformation of a vector in body-axes into a vector in wind-axes. Angles of attack and sideslip angles are output in radians.

## Examples

Determine the angle of attack and sideslip angle from direction cosine matrix:

```dcm = [ 0.8926 0.1736 0.4162; ... -0.1574 0.9848 -0.0734; ... -0.4226 0 0.9063]; [alpha beta] = dcm2alphabeta(dcm) alpha = 0.4363 beta = 0.1745```

Determine the angle of attack and sideslip angle from multiple direction cosine matrices:

```dcm = [ 0.8926 0.1736 0.4162; ... -0.1574 0.9848 -0.0734; ... -0.4226 0 0.9063]; dcm(:,:,2) = [ 0.9811 0.0872 0.1730; ... -0.0859 0.9962 -0.0151; ... -0.1736 0 0.9848]; [alpha beta] = dcm2alphabeta(dcm) alpha = 0.4363 0.1745 beta = 0.1745 0.0873```