| 计算Legendre函数导数的非奇异方法 |
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| 引用本文： | 于锦海,万晓云.计算Legendre函数导数的非奇异方法[J].测绘学院学报,2010(1). |
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| 作者姓名： | 于锦海 万晓云 |
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| 作者单位： | 中国科学院研究生院地球科学学院;中国科学院测量与地球物理研究所; |
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| 基金项目： | 国家自然科学基金资助项目(40674039) |
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| 摘 要： | 引力场关于经度和纬度方向的梯度在两极附近会产生奇异性现象,这将会给诸如重力场和静态洋流探索(GOCE,Gravity field and stesdy-state Oceam Circulation Explorer)数据处理等引力场的研究工作带来诸多不便和困难。这里首先分析了该奇异性产生的原因,即目前采用的球坐标系自身在两极处是奇异的;然后利用Legendre函数的性质推导了一组不含任何奇异性的计算引力场梯度的计算公式;最后与常用的迭代方法进行了实例计算比较,结果表明所导出的公式不仅计算精度大大提高,而且计算用时也不会增加。
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| 关 键 词： | GOCE卫星计划 奇异性 勒让德函数 迭代方法 引力场 |
Non-Singular Formulae for Computing Derivatives of Legendre Functions |
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| YU Jin-hai,WAN Xiao-yun.Non-Singular Formulae for Computing Derivatives of Legendre Functions[J].Journal of Institute of Surveying and Mapping,2010(1). |
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| Authors: | YU Jin-hai WAN Xiao-yun |
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| Institution: | 1;2;1.Earth College;Graduate University of Chinese Academy of Sciences;Beijing 100049;China;2.Institute of Geodesy and Geophysics;Chinese Academy of Sciences;Wuhan 430077;China |
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| Abstract: | Since the singularities occur near the poles in computing gradients of the gravitational field,this can cause a lot of difficulties in dealing with the gravitational field's data such as GOCE.In order to overcome the so-called singularities,the reasons for the singularities are analyzed firstly,i.e.,it is caused by adopting the spherical coordinates that are singular at the poles in mathematical meaning.Then non-singular computational formulae for derivatives of the Legendre's functions are derived with the... |
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| Keywords: | GOCE mission singularity Legendre's function iterative arithmetic gravitational field |
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