IAU 1980 nutation model
In 1979, J.Wahr and H.Kinoshita introduced re-comprehensive calculation for a practical nutation of the earth, they considered the force generated from earth’s solid tide to earth itself --- deformation, nutation and rotation rate changes, and at the same time, they
thought about the natural effect and ellipse sphere delaminating effect in the matter of three main layers of the earth. They drew a conclusion in 1980, we call it “IAU 1980 nutation theory”[5].





HERING nutation model
The HERRING nutation model[1] in this software will compute the complete KSV_1996_3 nutation series with the associated corrections for planetary nutation, the freely excited Free- Core-Nutation (FCN), the precession constant change and a rate of change of obliquity. This model is designed from several aspects as following:

1) The Souchay and Kinoshita Rigid Earth KSRE95 nutation series;
2) Factors of the Retrograde FreeCore Nutation (RFCN) resonance factors from the nutation formula the Mathews et al.
3) The effects of annual modulation of geodetic precession;
4) A prograde annual nutation has been estimated along with the resonance coefficients;
5) The free RFCN mode was estimated once every two years for the data after 1984;
6) The new Simons et al., fundamental arguments are used in this version.

MHB_2000 nutation model
VLBI and LLR observations[6] showed that there are obvious defect existing in the IAU 1976 precession model and IAU 1980 nutation theory which have been the criterion for a long time. For example, these theoretical model doesn’t include the changing rate of obliquity in nutation that can’t be observed; the precession rate exists the difference about -3.0mas/yr between observation value and adoption value (the adoption value is too high); for nutation, the difference between observation model and adoption model exists about 20mas between each top. In short, the difference between the observations and models used in the past has exceeded the achieved observation precision far more. We need to get the nutation theory with including ocean tide’s and atmosphere’s non-rigid body and all in the order of magnitude of 0.1mas level known effect, and get the nutation series reaching the level of 5mas new rigid body earth. Based on many years of research, IAU 2000 convention[7] decided that the newly IAU 2000A precession-nutation model, that is MHB_2000 model (up to the level of the accuracy of 0.2mas) and IAU 2000B precession-nutation model (up to the level of the accuracy of 1mas) will replace the IAU 1976 precession model and IAU 1980 nutation theory. Improved precession rate, obliquity nutation changing rate, as well as the Celestial pole offsets consistent with newly precessionnutation model on J2000.0 epoch will be given in IERS 2003 convention.

MHB_2000 model[8] was proposed by Mathews, and it was developedon the basis of setting the problem of linear dynamic equation for wobbly nutation. It uses the estimated value of 7 parameters in the theory, obtains one newly precession-nutation VLBI data sequence in the theory of least squares. This nutation sequence depends on rigid earth nutation sequence found by Souchay (1999). It explains the change of geodynamical ellipticity implied by the observing correction of equator lunar-solar precession by the multiplier of 1.000012249. The new model contains the deviation between reference frames, geodetic precession and geodetic nutation. The Free Core Nutation (FCN) can’t be strictly forecast, so this model doesn’t include it. New precession-nutation model avoids the artificial separation in precession and nutation, but the precession model and nutation model is used separately in the system based on the spring equinox.

Tidal fluctuations in water height and currents will induce retrograde diurnal variation of equatorial oceanic angular momentum (OAM), hence small perturbation on nutation at the level of 1mas and most important contributions come from water height variations[9]. Considering the influence of anelasticity covering effect, the ocean tidal effect, electromagnetism coupling effect, which produced from the liquid outer core and solid core and the nonlinearity item. The MHB_2000 nutation model improves the accuracy of IAU 1980 nutation theory.