Rotated System

) to define rotation about the out-of-plane axis in 2D and Euler angles in 3D.

In the window for define the rotation relative to the global Cartesian coordinate system. In 3D models, you specify the local coordinate system (xl, yl, zl) using three consecutive Euler angles (rotation angles) α, β, and γ. See Figure 5-4.

The transformation matrix for the 3D case is then

In 2D models, you describe the rotated coordinate system by the rotation angle about the out-of-plane vector. In both cases the origin of the coordinate system can be defined.

If this coordinate system is added as a subnode to a node, define where it will be active using a selection in the section. Also, the and fields are not available in this case.

In the 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.

Specify the location of the origin of the rotated coordinate system. Define it as a vector with two (for 2D) or three (for 3D) components. The default is the origin for the global Cartesian coordinate system. Using another origin translates the coordinates in the rotated system by that distance from the global Cartesian origin.

For 2D models, select an out-of-plane axis from the list (first, second, or third coordinate direction into or out-of screen), and then if necessary adjust the base vectors in the table under . Enter the (in radians). The default is 0.

For 3D models, enter the (in radians) in the α, β, and γ fields (see the graphics in the window for definitions of these angles). The default values are 0 for all angles.

This section is available in 3D, if you have added any work plane to the geometry.

From the list, select (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 , , and are used for the definition of the rotated system.