# quat2dcm

Convert quaternion to direction cosine matrix

## Description

example

dcm = quat2dcm(q) calculates the direction cosine matrix, n, for a given quaternion, q.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. This function normalizes all quaternion inputs.

## Examples

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Determine the direction cosine matrix from the single quaternion q = [1 0 1 0].

dcm = quat2dcm([1 0 1 0])
dcm = 3×3

0         0   -1.0000
0    1.0000         0
1.0000         0         0

Determine the direction cosine matrices from multiple quaternions.

q = [1 0 1 0; 1 0.5 0.3 0.1];
dcm = quat2dcm(q)
dcm =
dcm(:,:,1) =

0         0   -1.0000
0    1.0000         0
1.0000         0         0

dcm(:,:,2) =

0.8519    0.3704   -0.3704
0.0741    0.6148    0.7852
0.5185   -0.6963    0.4963

## Input Arguments

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Quaternion, specified as an m-by-4 matrix containing m quaternions. Each element of q must be a real number.

Data Types: double

## Output Arguments

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Direction cosine matrices, returned as a 3-by-3-by-m matrix, where m is the number of direction cosine matrices. The direction cosine matrix performs the coordinate transformation of a vector in inertial axes to a vector in body axes.

## Version History

Introduced in R2006b