Abstract
Almost three decades ago, the problem of long-term polar wander on a dynamic planet was formulated and simplified within the framework of normal mode theory. The underlying simplifications have been debated ever since, recently in a series of papers by Hu et al. (2017a, , 2017b, , 2019, ), who clarify the role of neglecting short-term relaxation modes of the body.
However, the authors still do not solve the governing equations in full, because they make approximations to the Liouville equation (LE). In this paper, I use a time domain approach and, for previously studied test loads, both the planet's relaxation and the LE are solved in full.
In order to analyze the existing LE approximations, I compute the energy balance of true polar wander (TPW). For fast rotating bodies such as Earth, the rotation axis becomes aligned with the main inertia axis (omega||MIA) once free oscillations are damped.
The omega||MIA assumption is re-derived theoretically-contrary to previous beliefs, I demonstrate that it is not necessarily linked to the quasi-fluid limit of the viscoelastic response to loading and rotation, but that it is an expression of neglecting the Coriolis and Euler forces from the equation of motion. It is thus important to distinguish between simplifying the LE and simplifying the planet's response to forcing.
For slow rotators such as Venus, the full LE together with energy analysis indicate that previous estimates of TPW rate need to be revisited. The numerical code LIOUSHELL is released on GitHub.