Define a Base Vector System () using a set of base vectors to form a coordinate system. The system does not necessarily need to be orthonormal, but when it is, declaring it orthonormal and linear enables simplifications that improve performance.

A vector F is represented by its contravariant components [F1, F2, F3]T in the base of the new base vector system defined by the base vectors u1, u2, and u3 on the form F = F1u1 + F2u2 + F3u3. Expressing the base vectors as components in another system (for example, the global spatial system [ex, ey, ez]) gives the transformation matrix between bases:

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. Note that these coordinate names are only used as indices for vector and tensor variable names, and cannot be evaluated as variables.

Define the Base vectors in terms of the global Cartesian coordinates (typically x, y, and z); one base vector on each row (two for 2D and three for 3D).

For some applications, only orthonormal coordinate systems can be used. Since the base vectors entered in a Base Vector System node are not necessarily orthonormal, these systems are by default not allowed in contexts requiring orthonormality. To make the coordinate system available in such contexts, select either the Assume orthonormal check box or the Make orthonormal check box. The former instructs automatic variable transforms to use the entered Base vectors directly, but treat them as orthonormal — if they are not, results will be incorrect. The Make orthonormal check box enables a polar decomposition of the base vector matrix into a rotation matrix and a stretch matrix. The rotation matrix — which is orthonormal — is kept, while the stretch matrix is discarded. This procedure is computationally more expensive than assuming orthonormality but guarantees a truly orthonormal transformation matrix that will behave correctly in subsequent variable transforms.

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 base vector.