Stress field and spin axis relaxation for inelastic triaxial ellipsoids

TL;DR

This paper derives a singularity-free formula for the stress tensor in inelastic, self-gravitating triaxial ellipsoids, providing new insights into energy dissipation and wobble dynamics in celestial bodies.

Contribution

It introduces a compact, singularity-free stress tensor formula for triaxial ellipsoids and applies it to analyze energy dissipation and spin axis relaxation.

Findings

Derived a compact stress tensor formula without singularities.

Compared damping times with previous models, showing smaller differences.

Validated the model against ellipsoid of revolution cases.

Abstract

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.