As is illustrated in Figure 3, a new, molecule-fixed coordinate system
must be developed. First, a vector,
, which points from our
external, lab fixed coordinate system to the center of mass of our
molecule. This point, O, will be the origin in our molecule-fixed coordinate
system. The rotation of the molecule-fixed coordinate system will
also be described by three Eulerian angles, 
, 
, and 
.
Another vector starting at O, 
, points to the current
position of atom 
. The equilbrium position of atom
is indicated by 
. This permits a displacement vector,
, to be defined as follows:
The total velocity of the atom can be defined as:
Where 
is the rotational velocity of the axis system.