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Effects of dissipation and a liquid core on forced nutations in Hamiltonian theory |
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| Authors: | Juan Getino & José M Ferrándiz |
| Institution: | Grupo de Mecánica Celeste, Facultad de Ciencias, 57005 Valladolid, Spain. E-mail:; Departamento de Matemática Aplicada, Escuela Politécnica Superior, 03080 Alicante, Spain. E-mail: |
| Abstract: | In a previous paper, the authors considered the free rotation of an earth model composed of a rigid mantle and a liquid core in the presence of dissipation 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 obtained in the former paper playing the role of the unperturbed solutions required in the application of the method. These solutions are consistent in the sense that, with the usual terminology, the rigid body solutions and the 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 perspective, we discuss the issue of the resonance in this context. The presence of dissipation changes dramatically the character of the FCN wobble; that is, it is no longer a regular oscillation but a damped one. A strict resonance phenomenon cannot take place thereby, since the forcing perturbations are oscillations with a real (non-complex) frequency. |
| Keywords: | dissipation forced nutations Hamiltonian theory liquid core |