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Differences in interpretation may arise from differences in formulation of the equations of celestial mechanics. This paper focuses on the Liouville system of differential equations. In a "modern" presentation of the equations, variations in polar motion (PM) and variations in length of day (lod) are decoupled. Their source terms result from redistribution of masses and torques. Elasticity of the Earth, large earthquakes, or external forcing by the fluid envelopes have been successively invoked in the "modern" approach. In the "classical" presentation, PM is governed by the inclination of Earth's rotation pole and the derivative of its declination (close to the derivative of lod). These are coupled by the Liouville system and all "source" terms are astronomical. The "classical" approach also implies that there should be a link between the rotations and the torques exerted by the planets of the solar system. A sufficiently strong source of energy can be found. There is remarkable agreement between the sum of forces exerted by the four Jovian planets and components of Earth's polar motion. Since 1970, lod tends to decrease, but a recent acceleration of rotation velocity, that contradicts previous models, finds a simple explanation with the "classical" formalism. Analysis of lod finds nine components, all with physical sense: first comes a "trend", then pseudo-oscillations with periods 80 yr , 18.6 yr, 11 yr , 1 year and 0.5 yr, 27.54 days, 13.66 days, 13.63 days and 9.13 days. The longer periods, 1 yr, 11 yr, 18.6 yr and 80 yr are common to lod and PM. The Liouville system of equations in the "classical" analysis implies a strong link between the two: the straightening of the inclination of the axis of rotation should accompany a decrease in lod.Also, if this link is valid, all the components with extraterrestrial periods should be present in the series of sunspots and indeed they are.