General-relativistic perturbation equations for the dynamics of elastic deformable astronomical bodies expanded in terms of generalized spherical harmonics

Abstract

In our previous paper, based on the Carter & Quintana framework and the Damour-Soffel-Xu scheme, we deduced a complete and closed set of post-Newtonian dynamical equations for elastically deformable astronomical bodies. In this paper, we expand the general relativistic perturbation equations of elastic deformable bodies (field equations, stress-strain relation, Euler equation) in terms of Generalized Spherical Harmonics. This turns the set of complicated partial differential equations into a set of ordinary differential equations. This will be useful for numerical applications that mainly deal with the global dynamics of the Earth.

arXiv comment11 pages

References in corpus (1)

• Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

Cited by in corpus (2)

• Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles