A simple mechanical model explaining the long-period (about 100-year) variations in the Earth's rotational velocity is proposed. This model takes into account the gravitational interaction of the mantle with the solid core of the Earth and the fact that the core rotation leads that of the mantle. The considered problem mathematically is reduced to a classical problem about nonlinear oscillator, being under the influence of the constant moment of forces. At values of the parameters answering of the core-mantle system there are a steady equilibrium state and a steady limiting cycle on the phase cylinder of this oscillator. The equilibrium state corresponds to a single angular velocity for the mantle and solid core with no long-period oscillations in the length of the day. The limiting cycle corresponds to the core rotation leading the mantle rotation. In this case, the ellipsoidality of the gravitationally interacting bodies provides a periodic interchange of kinetic angular momentum between the mantle and solid core, that results in long-period variations in the length of the day
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