# Documentation

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# eul2quat

Convert Euler angles to quaternion

## Syntax

``quat = eul2quat(eul)``
``quat = eul2quat(eul,sequence)``

## Description

example

````quat = eul2quat(eul)` converts a given set of Euler angles, `eul`, to the corresponding quaternion, `quat`. The default order for Euler angle rotations is `'ZYX'`.```

example

````quat = eul2quat(eul,sequence)` converts a set of Euler angles into a quaternion. The Euler angles are specified in the axis rotation sequence, `sequence`. The default order for Euler angle rotations is `'ZYX'`.```

## Examples

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```eul = [0 pi/2 0]; qZYX = eul2quat(eul) ```
```qZYX = 0.7071 0 0.7071 0 ```
```eul = [pi/2 0 0]; qZYZ = eul2quat(eul,'ZYZ') ```
```qZYZ = 0.7071 0 0 0.7071 ```

## Input Arguments

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Euler rotation angles in radians, specified as an n-by-3 array of Euler rotation angles. Each row represents one Euler angle set.

Example: `[0 0 1.5708]`

Axis rotation sequence for the Euler angles, specified as one of these character vectors:

• `'ZYX'` (default) – The order of rotation angles is z-axis, y-axis, x-axis.

• `'ZYZ'` – The order of rotation angles is z-axis, y-axis, z-axis.

• `'XYZ'` – The order of rotation angles is x-axis, y-axis, z-axis.

## Output Arguments

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Unit quaternion, returned as an n-by-4 matrix containing n quaternions. Each quaternion, one per row, is of the form q = [w x y z], with w as the scalar number.

Example: `[0.7071 0.7071 0 0]`