This information is part of the Modelica Standard Library maintained by the Modelica Association.

This type describes the rotation from a frame 1 into a frame 2. An instance R of type Orientation has the following interpretation:

T = [ex, ey, ez];
    e.g., T = [1,0,0; 0,1,0; 0,0,1]

where e_x,e_y,e_z are unit vectors in the direction of the x-axis, y-axis, and z-axis of frame 1, resolved in frame 2, respectively. Therefore, if v₁ is vector v resolved in frame 1 and v₂ is vector v resolved in frame 2, the following relationship holds:

v2 = T * v1

The inverse orientation T_inv = T^T describes the rotation from frame 2 into frame 1.

Since the orientation is described by 9 variables, there are 6 constraints between these variables. These constraints are defined in function TransformationMatrices.orientationConstraint.

Note, that in the MultiBody library the rotation object is never directly accessed but only with the access functions provided in package TransformationMatrices. As a consequence, other implementations of Rotation can be defined by adapting this package correspondingly.