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Published online by Cambridge University Press: 03 August 2017
A two-symmetric-rigid-rotators model of the Earth has been studied, under the hypothesis of elasto-viscous coupling. The free Eulerian equation of motion has been solved in the linear approximation related to small wobbling amplitudes. Under these hypotheses, polar motion is stable, and the angular velocity of the Earth is the sum of three vectors rotating with different frequencies and damped amplitudes. One of these terms turns out to be retrograde with a quasidiurnal frequency and could be identified with a similar term appearing in liquid core models of the Earth. The other two terms are identified with the Chandler wobble and the annual term according to observational data. The elastic coupling produces, in the time variation of L.O.D., a periodic term whose frequency is about one year. It could be hypothesized that the “decade fluctuation” could be partially attributed to the free oscillation of the Earth.