Forced nutations of the earth: Influence of inner core dynamics. I - Theory. II - Numerical results and comparisons. III - Very long interferometry data analysis

A treatment is presented of the nutation problem for an oceanless, elastic, spheroidally stratified earth, with the dynamical role of the inner core explicitly included in the formulation. Solving the enlarged system of equations shows that a new almost diurnal eigenfrequency emerges. A rough estimate places it not far from the prograde annual tidal excitation frequency, so that possible resonance effects on nutation amplitudes need careful consideration. Tables are provided that exhibit the sensitivities of various relevant quantities, the eigenfrequencies and the coefficients which appear in the resonance expansion, as well as the nutation amplitudes at important tidal frequencies, to possible errors in the earth parameters which enter the theory set forth. Finally, the analysis of 798 VLBI experiments performed between July 1980 and February 1989 and the determination from this analysis of corrections to selected coefficients in the International Astronomical Union 1980 theory of the nutations of the earth are discussed.