扰动重力梯度的非奇异表示

在局部指北坐标系中用地心球坐标来表示扰动重力梯度张量，当计算点趋近于两极时，由于Legendre函数的一阶和二阶导数以及分母上所含余纬的正弦函数，将导致扰动重力梯度张量的计算出现无穷大。因此，本文引入了Legendre函数的一阶和二阶导数以及 无奇异性的计算公式，并且进一步推导了 无奇异性的计算公式。在将Legendre函数的一阶和二阶导数以及 、 无奇异性的计算公式代入到扰动重力梯度张量各分量的求解中时，又充分考虑了m等于0，1，2以及其它量时的复杂情况，建立了扰动重力梯度张量各分量无奇异性的详细计算模型。通过模拟实验表明，本文所建立的详细计算模型不仅能够完全满足当前卫星重力梯度张量计算的精度要求，而且模型稳定、可靠、易于编程实现。

Non-singular Expression of the Disturbing Gravity Gradients

If the disturbing gravity gradients are expressed by earth-centered spherical coordinates in the local north-oriented reference frame, the first- and second-order derivatives of the Legendre functions of the colatitude and the sine function of colatitude in the denominator which tend to infinity when the computational point is approaching the poles. Therefore, the non-singular computational formulas of the first- and second-order derivatives of the Legendre functions of the colatitude and the are introduced, and the non-singular computational formula of is also deduced. When taking the non-singular computational formulas of the first- and second-order derivatives of the Legendre functions of the colatitude and the 、 into the computation of each component of the disturbing gravity gradients, the complex situation that the m equals to 0, 1, 2, and any other numerical values are also considered, and the non-singular particular computational models of each component of the disturbing gravity gradients are constructed. The simulation experimentation shows that the particular computational models constructed in this paper not only completely fulfill the precision demand of the computation of the current satellite gravity gradients, and the models are steady, credible and easy to be programmable realized.