Helmert Disturbing Potential and Its Integral Kernel Function with Ellipsoidal Harmonic Formula
-
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。
-
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
Abstract: 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. -
-
[1] 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 Heiskannen W A, Moritz H. Physical Geodesy[M]. Lu Fukang, Hu Guoli. Beijing: Surveying and Mapping Press, 1979
[2] 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 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
[3] 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 doi: 10.3321/j.issn:1001-1595.1997.02.013 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 doi: 10.3321/j.issn:1001-1595.1997.02.013
[4] 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 http://www.cqvip.com/QK/95685A/201406/663663594.html Zhang Chijun, Luo Mingjin, Liu Lintao. Solving Molodensky Problem with Ellipsoidal Function[J]. Journal of Geodesy and Geodynamics, 2014, 34(6):148-156 http://www.cqvip.com/QK/95685A/201406/663663594.html
[5] 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 http://www.cqvip.com/QK/93330B/201501/664464134.html 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 http://www.cqvip.com/QK/93330B/201501/664464134.html
[6] Abramowitz M, Stegun I. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathe-matical Tables[M]. New York: Dover Publications, 1970
[7] 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 doi: 10.1007/s00190-002-0271-8
[8] Heck B. On the Linearized Boundary Value Pro-blems of Physical Geodesy[D]. Ohio: Ohio State University, 1996
[9] Hobson E W. The Theory of Spherical and Ellipsoidal Harmonics[J]. Monatshefte für Mathematik und Physik, 1934, 41(1):A22 http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_0903.1049
[10] 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 http://ch.whu.edu.cn/CN/abstract/abstract4787.shtml 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 http://ch.whu.edu.cn/CN/abstract/abstract4787.shtml
[11] 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 http://ch.whu.edu.cn/CN/abstract/abstract213.shtml 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 http://ch.whu.edu.cn/CN/abstract/abstract213.shtml
[12] 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 http://ch.whu.edu.cn/CN/abstract/abstract1791.shtml 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 http://ch.whu.edu.cn/CN/abstract/abstract1791.shtml
[13] 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 http://ch.whu.edu.cn/CN/abstract/abstract3430.shtml 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 http://ch.whu.edu.cn/CN/abstract/abstract3430.shtml
计量
- 文章访问数: 1989
- HTML全文浏览量: 152
- PDF下载量: 225
下载:
