Free Inner Core Nutation (FICN) or prograde FCN (PFCN)
This motion is very similar to the FCN, but concerns the outer and
inner core. It has never been observed and theoretical calculations
predict a very weak resonance effect on Earth tides and nutations.
The period is retrograde diurnal in the terrestial frame and prograde
long-period in the celestial frame (of about 470 days).
The parameters involved are the flattening of the inner core, the
densities of the inner core and outer core, and the deformation of the
Inner Core Boundary (ICB) due to the fluid dynamic pressure
on the ICB. In a very detailed analysis of VLBI data, Mathews et al.
(JGR, 2001) have determined a FICN period and damping from its resonance
in the nutations. They obtain a period of 1025 days.