EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

On the elastodynamics of rotating planets

Matthew Maitra1 and David Al-Attar2
Matthew Maitra and David Al-Attar
  • 1Institut für Geophysik, ETH Zürich, Switzerland (
  • 2Bullard Laboratories, University of Cambridge, Cambridge, UK

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.

How to cite: Maitra, M. and Al-Attar, D.: On the elastodynamics of rotating planets, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10327,, 2022.