Effects of dissipation and a liquid core on forced nutations in Hamiltonian theory

In a previous paper, the authors considered the free rotation of an earth m odel composed of a rigid mantle and a liquid core in the presence of dissip ation and under the Hamiltonian formalism, obtaining analytical expressions for the free nutation modes. In this paper we treat the forced motion. Approximate analytical solutions are worked out by means of Hori's perturbation method, the free solutions o btained in the former paper playing the role of the unperturbed solutions r equired in the application of the method. These solutions are consistent in the sense that, with the usual terminology, the rigid body solutions and t he complex transfer functions are calculated with the same parameters. Besides in-phase terms, the dissipation at the core-mantle boundary studied in this paper gives rise to out-of-phase terms. From a qualitative perspec tive, we discuss the issue of the resonance in this context. The presence o f dissipation changes dramatically the character of the FCN wobble; that is , it is no longer a regular oscillation but a damped one. A strict resonanc e phenomenon cannot take place thereby, since the forcing perturbations are oscillations with a real (non-complex) frequency.