When the motion of a multiple rigid body system can be described as two rotations about two different pivots, the modulation of the PCS becomes more complicated. Figure 12.1 shows this motion for a single lanthanide to atom vector.
The six vectors at the original position are
The six vectors after the first rotation for state i, Ri(1), are
The six vectors after the second rotation for state i, Ri(2), are
As defined in equation 12.59 on page , the PCS for state i is
|δ = riT⋅A⋅ri.||(12.64)|
For the double motion of the lanthanide-atom vector rLN(2), this becomes
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