微椭弹性地球运动的一个边界条件的推导

THE DERIVATION OF A SCALAR BOUNDARY CONDITION FOR THE MOTION OF THE ELASTIC AND SLIGHTLY ELLIPTICAL EARTH

在研究地球章动或潮汐理论时 ,常常需要对均匀自转、微椭、弹性、自引力的地球的运动方程组积分 ,并通过选取一组恰当的边界条件来定解 .在一阶扁率近似下 ,先将椭球形参考边界上一个有关形变的连续量转化到等效球面上 ,然后作广义面球谐函数展开进行标量化 ,并分解为球形与环形部分 ,截断后可导出 3个标量常微分形式的边界条件 .

The scalar equations of infinitesimal elastic gravitational motion for a rotational, slightly elliptical Earth are always used to study the Earth's nutation and tides theoretically, while the determination of the integration of the equations depends, in a certain extent, upon the choice of a set of boundary conditions. In this paper, a continuous quantity related to the displacement is transformed from the elliptical reference boundary to the corresponding effective spherical domain, and 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 the poloidal and toroidal fields. After being truncated, the boundary conditions are derived, at last, in scalar ordinary differential format. The procedure of the derivation is in the order of the ellipticity and in full details.