  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.
