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

Chongming Xu·Xuejun Wu·Michael Soffel
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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.

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Chongming Xu, Xuejun Wu, Michael Soffel. 2005-10-08. General-relativistic perturbation equations for the dynamics of elastic deformable astronomical bodies expanded in terms of generalized spherical harmonics. https://doi.org/10.1103/physrevd.71.024030

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