The Input Base Vector System

This is the system used by all spatial (length 3) vector-valued and tensor-valued user inputs. The options in the list are the same as The Base Vector System list. When the settings differ between these two lists, everything a user enters for a user input, is automatically transformed to the system defined by the list. The transformation matrices used by the transformation can be accessed through a special scope syntax, sys.<variable>. There are six variables defined by a coordinate system that you can access using this scope. These are summarized in the table below:


Variable	Symbol	Description	Base Vector system
T		Transformation matrix from public system to global system for contravariant tensors	i: public system j: global system
invT		Transformation matrix from global system to public system for contravariant tensors	i: global system j: public system
gSup	gij	Contravariant metric tensor for public system with respect to global system	i, j: public system
gSub	gij	Covariant metric tensor for public system with respect to global system	i, j: public system
detT		Determinant of T, and also the volume of a unit cube in the public system measured in the global system	Not applicable
detInvT		Determinant of invT, and also the volume of a unit cube in the global system measured in the public system	Not applicable

The public system of a coordinate system is the base vector system it defines and the global system is the base vector system the public system is defined with respect to. A global system is almost always also a frame system, whose base vectors represents the coordinates of a frame. For example, a rotated system performs a rotation of the base vectors of the global system to get the base vectors of the public system.

In some special situations, the global system of the selected coordinate system can differ from the global system of the base vector system used by the feature or property. In those cases, the transformation matrices include an extra transformation between the different global systems. Because the global systems also are frame systems, these extra transformations are usually called frame transformations. A frame transformation between the material frame and the spatial frame is given by the differentiation of the spatial coordinate with respect to the material coordinates or vice versa.