解混合边值问题直接计算位系数的变分原理

A Variational Principle for Solving the mixed boundary Value Problem and Calculating Directly the Potential Coefficients

本文提出了利用变分法解混合边值问题直接计算位系数的原理。根据这一原理可解第一、第二和第三边值问题的混合边值问题直接求得位系数。利用这一原理可较简单地联合利用经典重力测量(即重力点的平面位置由天文或三角测量确定,高程由水准或三角高程确定)、卫星重力测量(即利用卫星定位技术确定重力点的平面位置和大地高)以及卫星测高数据研究地球的重力场。

A variational principle is presented in this paper for directly calculating the potential coefficients in solving the mixed boundary value problem. According to the principle, potential coefficients can be obtained directly in solving the mixed boundary value problems of first, second and third type. The principle can be used for studying Earth' s gravity field jointly applying the classical gravimetric(the gravimetric points are positioned using classical geodetic method such as trianglation and geometric levelling), satellite gravimetric (the gravimetric points are positioned by satellite positioning techniques) and satellite altimetric data.