# 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:

$\vec{u} = \mathbf{R}_{\theta}^{a} \cdot (\vec{X}- \vec{P}_0) + \vec{P} -\vec{X},$

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 $$2*pi*t$$

Rotation of the unit cube around the z-Axis with additional translation of the base point
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}