On the elastodynamics of rotating planets

We present a theoretical framework for modelling the rotational dynamics of solid elastic bodies. It takes full account of: Earth’s variable rotation, aspherical topography, and lateral variations in density and wave-speeds. It is based on an exact decomposition of the body’s motion that separates out the motion’s elastic and rotational components, in a way that we will make precise. As a prelude to the elastic problem, we show how Hamilton’s principle provides an elegant means of deriving the exact and linearised equations of rigid body motion, then study the normal modes of a rigid body in uniform rotation. We subsequently build on these ideas to write down the exact equations of motion of a variably rotating elastic body. We linearise the equations and discuss their numerical solution, before showing how to extend these ideas to analyse N elastic bodies interacting through gravity. We finally discuss the extensions that would be necessary in order to describe layered fluid-solid bodies, and discuss the applications of this work to problems of Earth rotation.