  In this study, we formulated a triaxial three-layered anelastic Earth
rotation theory con-sidering various core mantle couplings, including the
pressure and gravitational couplings acting on the inner core by the outer core
and mantle, the viscoelectromagnetic couplings between the outer core and
mantle, and between the outer and inner cores. With this formulation, we
provided four numerical solutions for the rotational normal modes, including
the Chandler Wobble (CW), Free Core Nutation (FCN), Free Inner Core Nutation
(FICN), an the Inner Core Wobble (ICW). The triaxiality led to increased
periods for the CW and ICW of about 0.01 and 0.35 mean solar days (d),
respectively. The mantle anelasticity and ocean tide induced dissipations were
mainly responsible for the CW, but contributed little to the FCN, while the
viscoelectromagnetic coupling induced dissipations were mainly responsible for
the FCN, FICN, and ICW. By investigating different types of couplings, we found
that pressure coupling played the dominant role in prograde FICN, while
viscoelectromagnetic or gravitational couplings either alone, or together gave
rise to retrograde FICN. On the other hand, the ICW period varied extensively
from 130 d to 21 yr under different core mantle coupling conditions.
