Helmert扰动位及其积分核函数的椭球实用公式  

Helmert Disturbing Potential and Its Integral Kernel Function with Ellipsoidal Harmonic Formula

作　　者：魏子卿 杨正辉[1] WEI Ziqing;YANG Zhenghui(School of Geological Engineermg and Geomaties,Chang'an University,Xi'an 710054,China;Xi'an Research Institute of Surveying and Mapping,Xi'an 710054,China)

机构地区：[1]长安大学地质工程与测绘学院,陕西西安710054 [2]西安测绘研究所,陕西西安710054

出　　处：《武汉大学学报（信息科学版）》2018年第12期1768-1774,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41674025)~~

摘　　要：借助以地心参考椭球面为边界面的第二大地边值问题的理论,基于Helmert空间的Neumann边值条件,给定Helmert扰动位的椭球解表达式,并详细推导第二类勒让德函数及其导数的递推关系、Helmert扰动位函数的椭球积分解以及类椭球Hotine积分核函数的实用计算公式,便于后续椭球域第二大地边值问题的实际研究。Based on the theory of the Neumann boundary value problem of geodesy on the geocentric reference ellipsoid as the boundary surface. In the Helmert space, derive the ellipsoidal series expansion of harmonic functions outside the referential ellipsoidal, the relationship of second kinds of associa-ted Legendre functions and its derivatives recurrence formula, Helmert disturbing potential and its integral kernel function with ellipsoidal harmonic formula,in order to research the Neumann boundary value problem of geodesy in the ellipsoidal coordinates.

关 键 词：NEUMANN边值问题 Helmert扰动位 第二类勒让德函数 椭球积分解 类椭球Hotine积分核函数 

分 类 号：P223[天文地球—大地测量学与测量工程]