# simscape.multibody.QuaternionRotation class

Package: simscape.multibody
Superclasses: simscape.multibody.Rotation

Construct rotation by using unit quaternion

## Description

Use an object of the simscape.multibody.QuaternionRotation class to construct a 3-D rotation by using a quaternion object. A quaternion object is a four-element unit vector,

$Q=\left(\begin{array}{cc}S& V\end{array}\right)$,

where:

$S=\mathrm{cos}\left(\frac{\theta }{2}\right)$,

and

$V=\left[{U}_{x}\text{\hspace{0.17em}}{U}_{y}\text{\hspace{0.17em}}{U}_{z}\right]\mathrm{sin}\left(\frac{\theta }{2}\right)$.

θ is the angle of rotation and [Ux, Uy, Uz] is the unit vector of the rotational axis. Note that for any given rotation, there are two quaternions that are negatives of each other, but represent the same rotation. For example, the quaternions [1 0 0 0] and [-1 0 0 0] both represent the identity rotation.

### Class Attributes

 Sealed true ConstructOnLoad true RestrictsSubclassing true

For information on class attributes, see Class Attributes.

## Creation

### Description

R = simscape.multibody.QuaternionRotation creates a rotation with default quaternion.

R = simscape.multibody.QuaternionRotation(Q) creates a rotation with the specified quaternion.

## Properties

expand all

Unit quaternion, specified as a quaternion object that represents a four-element unit vector.

Example: 0.70711 + 0.40825i + 0.40825j + 0.40825k

#### Attributes:

 GetAccess public SetAccess public NonCopyable true

## Version History

Introduced in R2022a