# quat2eul

Convert quaternion to Euler angles

## Syntax

``eul = quat2eul(quat)``
``eul = quat2eul(quat,sequence)``
``[eul,eulAlt] = quat2eul(___)``

## Description

````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"`. ```

example

````[eul,eulAlt] = quat2eul(___)` also returns an alternate set of Euler angles that represents the same rotation `eulAlt`.```

## Examples

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```quat = [0.7071 0.7071 0 0]; eulZYX = quat2eul(quat)```
```eulZYX = 1×3 0 0 1.5708 ```
```quat = [0.7071 0.7071 0 0]; eulZYZ = quat2eul(quat,'ZYZ')```
```eulZYZ = 1×3 -1.5708 1.5708 1.5708 ```

## Input Arguments

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Unit quaternion, specified as an n-by-4 matrix or n-element vector of `quaternion` objects containing n quaternions. If the input is a matrix, each row is a quaternion vector 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 string scalars:

• `"ZYX"` (default)

• `"ZYZ"`

• `"ZXY"`

• `"ZXZ"`

• `"YXY"`

• `"YZX"`

• `"YXZ"`

• `"YZY"`

• `"XYX"`

• `"XYZ"`

• `"XZX"`

• `"XZY"`

Each character indicates the corresponding axis. For example, if the sequence is `"ZYX"`, then the three specified Euler angles are interpreted in order as a rotation around the z-axis, a rotation around the y-axis, and a rotation around the x-axis. When applying this rotation to a point, it will apply the axis rotations in the order x, then y, then z.

Data Types: `string` | `char`

## 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]`

Alternate Euler rotation angle solution 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]`

## Version History

Introduced in R2015a

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