# angle2quat

Convert rotation angles to quaternion

## Syntax

```quaternion = angle2quat(rotationAng1,rotationAng2,rotationAng3) quaternion = angle2quat(rotationAng1,rotationAng2,rotationAng3,rotationSequence) ```

## Description

`quaternion = angle2quat(rotationAng1,rotationAng2,rotationAng3)` calculates the quaternion for three rotation angles. Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. The rotation used in this function is a passive transformation between two coordinate systems.

`quaternion = angle2quat(rotationAng1,rotationAng2,rotationAng3,rotationSequence)` calculates the quaternion using a rotation sequence.

## Input Arguments

`rotationAng1`

`m`-by-1 array of first rotation angles, in radians.

`rotationAng2`

`m`-by-1 array of second rotation angles, in radians.

`rotationAng3`

`m`-by-1 array of third rotation angles, in radians.

`rotationSequence`

Rotation sequence. For example, the default `'ZYX'` represents a sequence where `rotationAng1` is z-axis rotation, `rotationAng2` is y-axis rotation, and `rotationAng3` is x-axis rotation.

 `'ZYX'` `'ZYZ'` `'ZXY'` `'ZXZ'` `'YXZ'` `'YXY'` `'YZX'` `'YZY'` `'XYZ'` `'XZY'` `'XYX'` `'XZX'` `'ZYX'` (default)

## Output Arguments

 `quaternion` `m`-by-4 matrix containing `m` quaternions. `quaternion` has its scalar number as the first column.

## Examples

Determine the quaternion from rotation angles:

```yaw = 0.7854; pitch = 0.1; roll = 0; q = angle2quat(yaw, pitch, roll) q = 0.9227 -0.0191 0.0462 0.3822```

Determine the quaternion from rotation angles and rotation sequence:

```yaw = [0.7854 0.5]; pitch = [0.1 0.3]; roll = [0 0.1]; q = angle2quat(pitch, roll, yaw, 'YXZ') q = 0.9227 0.0191 0.0462 0.3822 0.9587 0.0848 0.1324 0.2371``` 