# Documentation

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# quat2eul

Convert quaternion to Euler angles

## Syntax

``eul = quat2eul(quat)``
``eul = quat2eul(quat,sequence)``

## Description

example

````eul = quat2eul(quat)` converts a quaternion rotation, `quat`, to the corresponding Euler angles, `eul`. The default order for Euler angle rotations is `'ZYX'`.```

example

````eul = quat2eul(quat,sequence)` converts a quaternion into Euler angles. 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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```quat = [0.7071 0.7071 0 0]; eulZYX = quat2eul(quat) ```
```eulZYX = 0 0 1.5708 ```
```quat = [0.7071 0.7071 0 0]; eulZYZ = quat2eul(quat,'ZYZ') ```
```eulZYZ = 1.5708 -1.5708 -1.5708 ```

## Input Arguments

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Unit quaternion, specified 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]`

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

Example: `[0 0 1.5708]`