# Rotating Motion

The *rotating motion* constraint is used to define a rigid body rotation of the assigned entities. The user can define the rotation axis, the base point and the rotation angle. Each component can be defined as a *formula* or *table* value.

If Raθ denotes the rotation matrix of a general rotation about the axis with an angle of θ, then the displacement u⃗ of a point X⃗ is calculated as:

u⃗ =Raθ⋅(X⃗ −P⃗ 0)+P⃗ −X⃗

where P⃗ denotes the axis base point and P⃗ 0 it’s position at time t=0.0.

## Base Point

This point is the base point for the rotation axis. A possible movement of the base point with respect to the initial position at time t=0.0 during the rotation process is taken into account.

## Rotation Axis

The rotation axis is defined by its three components in the global coordinate system.

Important

If a component of the rotation axis is given as formula or table value the user has to make sure that the length of the axis vector is always positive.

## Rotation Angle

The rotation angle is defined in a mathematical positive sense around the rotation axis.

Important

If a continuous, transient rotation is required the rotation angle has to be given either as a formula or table value.

## Example

In the example below a unit cube was rotated with 60 rpm around the z-Axis with a base point moving in positive z-direction with 1m/s. The bottom face was assigned and the corresponding settings were:

- Base Point (0,0,t)

$(0,0,t)$

- Rotation axis (0,0,1)

$(0,0,1)$

- Rotation angle 2∗pi∗t

Rotation of the unit cube around the z-Axis with additional translation of the base point