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# dcm2quat

Convert direction cosine matrix to quaternion

q = dcm2quat(n)

## Description

q = dcm2quat(n) calculates the quaternion, q, for a given direction cosine matrix, n. Input n is a 3-by-3-by-m matrix of orthogonal direction cosine matrices. The direction cosine matrix performs the coordinate transformation of a vector in inertial axes to a vector in body axes. q returns an m-by-4 matrix containing m quaternions. q has its scalar number as the first column.

## Examples

Determine the quaternion from direction cosine matrix:

```dcm = [0 1 0; 1 0 0; 0 0 1];
q = dcm2quat(dcm)

q =

0.7071         0         0         0```

Determine the quaternions from multiple direction cosine matrices:

```dcm        = [ 0 1 0; 1 0 0; 0 0 1];
dcm(:,:,2) = [ 0.4330    0.2500   -0.8660; ...
0.1768    0.9186    0.3536; ...
0.8839   -0.3062    0.3536];
q = dcm2quat(dcm)

q =

0.7071         0         0         0
0.8224    0.2006    0.5320    0.0223```