Axial near - Symmetry , Angular Momentum , and Polar Excitation

The mechanism of the excitation of the Earth's polar instability in the absence of external torques is explored. The conventional perturbation scheme used to simplify the Liouville equation has oversimplified the excitation physics. The Earth becomes axially near-symmetrical and slightly triaxial during polar excitation, which induces additional change in the moment of inertia. Polar excitation is due to mass redistribution in a part of the Earth to appear as a relative angular momentum involving both motion and rotation, while the rest of the Earth is only in rotation. Relative angular momentum arising due to mass redistribution consists of two terms; one is due to .-motion, and the other involves the products of inertia induced by the motion. Motion excites a wobble of the rotation axis around the principal axis. The products of inertia force the " instantaneous figure axis " to shift away from the principal axis to initiate secular polar shift, while the rotation axis continues to wobble around the " instantaneous figure axis " at its new position. Wobble can thus be excited alone by motion, but secular polar shift comes always along with a wobble and can only be excited by the products of inertia. The " residual " products of inertia induced by motion and the products of inertia arising due to axial near-symmetry constitute continued polar excitation. During continued polar excitation, the " instantaneous figure axis " around which the rotation axis wobbles will no longer be the principal axis. The principal axis will no longer be symmetrical, with its new location to be determined. New definition of relative I : angular momentum facilitates a simpler and physically more justified way to determine the angular momenta of different parts of the Earth, such as the atmosphere, oceans, outer core, earthquake and tectonic movements, or even meteorite impact, that involve motion. A meteorite impact is insignificant for polar excitation if its mass is not great enough to induce substantial products of inertia in the Earth. The relative angular momentum of the atmosphere does not have the physical inconsistencies as that of the conventional angular momentum function. True polar wandering in geologic history is expected to be small. The recent secular polar shift is unlikely attributable to the Earths viscoplastic response to the Pleistocene deglaciation.