扰动重力梯度的非奇异表示  

Non-singular Expression of the Disturbing Gravity Gradients

作　　者：刘晓刚[1] 吴晓平[1] 赵东明[1] 吴星[1] 

机构地区：[1]信息工程大学测绘学院,河南郑州450052

出　　处：《测绘学报》2010年第5期450-457,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40774031);全国优秀博士论文专项基金(200344);卫星导航与定位教育部重点实验室(B类)开放基金(GRC-2009010);中国科学院动力大地测量学重点实验室开放基金(L06-06);信息工程大学博士生创新基金

摘　　要：引入Legendre函数的一阶和二阶导数以及m-Pnm(cosθ)/sinθ无奇异性的计算公式,并且进一步推导m2P-nm(cosθ)/sin2θ无奇异性的计算公式。在将Legendre函数的一阶和二阶导数以及m-Pnm(cosθ)/sinθ、m2-Pnm(cosθ)/sin2θ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m等于0、1、2以及其他量时的复杂情况,建立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。The non-singular computational formulae of the first-and second-order derivatives of the Legendre functions of the colatitude and the m P-n m（cos θ）/sin θ are introduced,and the non-singular computational formula of m2P-n m（cos θ）/sin2 θ 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 m P-n m（cos θ）/sin θ,m2P-n m（cos θ）/sin2 θ 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,but also the models are steady,credible and easy to be programmable realized.

关 键 词：扰动重力 重力梯度 球谐系数 局部指北坐标系 GOCE 

分 类 号：P228[天文地球—大地测量学与测量工程]