Simplifying using Eckart conditions

There is a little problem with the expression for the kinetic energy we have a redundancy in the coordinates. Indeed, we have three coordinates for defining translation (/ cm) three that determine rotation (to) and on top of that M vectors r . Too many. Six are redundant. Using such coordinates would be very annoying, because we have to take into account that they are non-independent.  

We may impose six relations among the coordinates and in this way get rid of the redundancy. The first three relations are evident, because the origin of the BFCS is simply the centre of mass. Therefore, 

Inserting (6.31) and (6.32) into the kinetic energy expression makes the roto-translational and vibro-translational couplings vanish. Thus, we have 

And we would have to check all the time, whether their values are consistent. 

We complete get rid of the redimdanq if the second Eckart condition is imposed (equivalent to three conditions for the coordinates) 

---