# 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 \(\mathbf{R}_{\theta}^{a}\) denotes the rotation matrix of a general rotation about the axis \(a\) with an angle of \(\theta\), then the displacement \(\vec{u}\) of a point \(\vec{X}\) is calculated as:

where \(\vec{P}\) denotes the axis base point and \(\vec{P}_0\) 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 continous, 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 \((0,0,t)\)
- Rotation axis \((0,0,1)\)
- Rotation angle \(2*pi*t\)