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- 2018
Helmert扰动位及其积分核函数的椭球实用公式
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Abstract:
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
| [1] | Abramowitz M, Stegun I. Handbook of Mathematical Functions:With Formulas, Graphs, and Mathe-matical Tables[M]. New York:Dover Publications, 1970 |
| [2] | Zhang Chijun,Luo Mingjin,Liu Lintao. Solving Molodensky Problem with Ellipsoidal Function[J]. Journal of Geodesy and Geodynamics, 2014,34(6):148-156(张赤军,骆鸣津,柳林涛. 用椭球函数解Molodensky问题[J]. 大地测量与地球动力学,2014,34(6):148-156) |
| [3] | Heiskannen W A, Moritz H. Physical Geodesy[M]. Lu Fukang, Hu Guoli. Beijing:Surveying and Mapping Press, 1979(海斯卡涅W A,莫里斯H.物理大地测量[M]. 卢福康,胡国理.北京:测绘出版社, 1979) |
| [4] | Li Jiancheng, Chen Junyong, Ning Jinsheng,et al. The Theory of Earth Gravity Field Approximation and Determination of 2000 Quasi-Geoid in China[M].Wuhan:Wuhan University Press,2003(李建成,陈俊勇,宁津生,等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉:武汉大学出版社,2003) |
| [5] | Yu J,Jekeli C, Zhu M. Analytical Solutions of the Dirchlet and Neumann Boundary-Value Problems with an Ellipsoidal Boundary[J]. Journal of Geodesy, 2003,76:653-667 |
| [6] | Heck B. On the Linearized Boundary Value Pro-blems of Physical Geodesy[D]. Ohio:Ohio State University, 1996 |
| [7] | Hobson E W. The Theory of Spherical and Ellipsoidal Harmonics[J]. Monatshefte für Mathematik und Physik, 1934, 41(1):A22 |
| [8] | Zhang Liming, Li Fei, Yue Jianli. Effort of Gravity of Disturbance Precision on GPS Boundary Value Problem[J]. Geomatics and Information Science of Wuhan University, 2007, 34(1):15-18(张利明,李斐,岳建利. 扰动重力对GPS重力边值问题的影响研究[J]. 武汉大学学报·信息科学版, 2007, 34(1):15-18) |
| [9] | Wei Ziqing. Recurrence Relations for Fully Normali-zed Associated Legendre Functions and Their Deri-vatives and Integrals[J].Geomatics and Information Science of Wuhan University, 2016, 41(1):27-36(魏子卿. 完全正常化缔合勒让德函数及其导数与积分的递推关系[J]. 武汉大学学报·信息科学版, 2016, 41(1):27-36) |
| [10] | Zhang Chuanding, Lu Zhonglian,Wu Xiaoping. On the Ellipsoidal Possion,Hotine and Stokes' Integration Formula[J].Acta Geodaetica et Cartographica Sinica, 1997,26(2):176-183(张传定,陆仲连,吴晓平. 椭球域大地边值问题的实用解式[J]. 测绘学报,1997,26(2):176-183) |
| [11] | Wei Ziqing. An Introduction to the Second Geodetic Boundary Value Problem with Geocentric Reference Ellipsoid[J]. Journal of Surveying Science and Engineering, 2015,35(1):1-6(魏子卿.以地心参考椭球面为边界面的第二大地边值问题引论[J].测绘科学与工程,2015,35(1):1-6) |
| [12] | Li Jiancheng, Chao Dingbo. Derivation of Hotine Function Using Possion Integral and Application of Hotine Formula[J].Geomatics and Information Science of Wuhan University, 2003,28(S1):55-57(李建成,晁定波. 利用Possion积分推导Hotine函数及Hotine公式应用问题[J]. 武汉大学学报·信息科学版, 2003, 28(S1):55-57) |
| [13] | Jiang Tao, Wang Zhengtao, Li Dawei,et al. Fast Algorithm for the Discrete Summation of Stokes' and Hotine's Integral[J].Geomatics and Information Science of Wuhan University, 2012, 37(5):606-609(蒋涛,王正涛,李大炜,等.Stokes和Hotine积分离散求和的快速算法[J]. 武汉大学学报·信息科学版, 2012, 37(5):606-609) |
