Abstract
The scalar equations of infinitesimal elastic-gravitational motion for a rotating, slightly elliptical Earth are always used in the theoretical study of the Earth's nutation and tides, and the determination of the integration of the equations depends, to a certain extent, on the choice of a set of boundary conditions. In this paper, a continuous quantity related to the displacement is first transformed from the elliptical reference boundary to the corresponding effective spherical domain, and is converted from vector (or tensor) form to scalar form by generalized surface spherical harmonics expansion. All the related components, including the displacement field (or the stress tensor field), are then decomposed into a poloidal and a toroidal field. After truncation, the boundary conditions are derived in scalar ordinary differential form. The derivation is given in full detail.
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