Use a Rotated System () to define an orthonormal coordinate system which is rotated with respect to the reference system. In 2D, you can specify either an in-plane rotation angle or a full 3D rotation using Euler angles. In 3D, Euler angles (Z-X-Z) is the only option.

Full 3D rotations are specified as three consecutive Euler angles α, β, and γ, using a Z-X-Z convention. Rotation axes and angles are illustrated in Figure 5-4 where the resulting rotated system axes are denoted X, Y, and Z.

The transformation matrix defined by the Euler angles transforms components of a fixed vector v from the rotated coordinate system, [vX,vY,vZ], to components in the global system, [vx,vy,vz], as follows:

If this coordinate system is added as a subnode to a Combined System node, define where it will be active using a selection in the Geometric Entity Selection section. Also, the Name and Coordinate names fields are not available in this case.

In the Coordinate names table, the default names are entered — x1, x2, and x3. In planar 2D models, x1 and x2 are typically the in-plane coordinates, and x3 is the out-of-plane coordinate.

The rotation settings depend on the space dimension of the component to which the coordinate system belongs. For 2D components, first select an Input method: In-plane rotation (the default) or General rotation.

When the input method is set to In-plane rotation in a 2D component, you specify the rotation as a single angle (in radians) representing the Rotation about out-of-plane axis. The Out-of-plane axis can be set to any of the three main axes, pointing either into or out of the screen. The default for planar 2D geometries is Third out-of screen, which leaves the x and y axes as in-plane reference axes. For axisymmetric geometries, the default is Second out-of screen, leaving the r and z axes in-plane.

For 3D geometries and when General rotation has been chosen as input method in 2D, enter the Euler angles (Z-X-Z) (in radians) in the α, β, and γ fields (see the graphics in the Settings window for definitions of these angles). The default values are 0 for all angles.

From the Work plane list, select xy-plane (the default, for a standard global Cartesian coordinate system) or select any work plane in the geometry sequence. If you choose a work plane, the work plane’s coordinates xw, yw, and zw are used for the definition of the rotated system.