Following the previous post *here*, we use Jacobian matrices to transform location and chronation vectors between inertial observers.

As before, let matrices be written with upper case boldface. Let vectors be written in lowercase boldface and their scalar magnitude without it. Velocity = **V**, lenticity = **W**, displacement = **x**, distimement = **z**, independent distance = *s*, independent distime = *t*. Components are in lowercase italics with subscripts.

The expanded Galilean transformation for the length frame is:

The expanded Galilean transformation for the length frame is:

Motion can be considered a transformation. For example, free fall with acceleration **A** is:

where the matrix is multiplied by the distime vector twice. With relentation **B** it is:

where the matrix is multiplied by the distance vector twice.