摘要
重力空间与几何空间有着密切的联系。本文首先将拉格朗日应变张量引入几何位移场，借助点位几何向量与重力向量之间的局部可逆定理，建立了重力位二阶梯度与点位几何应变之间的一般关系式；特别是依据一个已知的正常椭球，我们得到了实际重力位曲率参数、正常椭球曲率参数以及扰动位引起的点位应变参数之间的简单关系。这些关系式，在大地测量研究中有着许多潜在的应用，尤其在与扰动位和水准面有关的变形分析方面，以及在时变重力位与时变大地水准面变形的分析方面。
:
Three exists close connection between gravity shape and geometric one. After introducing the concept of Lagrangian Strain tensor to geometric displacementn field, a general relation between the geometric strain of position and the second derivatives of gravity potential is established according to the local differential inverse theorem between geometric vector and gravity one. In particular, by referring a known normal ellipsoid, a simple equation system between the curvature parameters of actual gravity potential, those of normal ellipsoid and strain parameters of position caused by disturbing potential is obtained. These relations have great potential of finding application in geodesy, parti cularly in the deformation analysis related to diaturbing potential as well as in the ana lysis of time variations of gravity field and position
出处
《测绘学报》
EI
CSCD
北大核心
1990年第3期187-192,共6页
Acta Geodaetica et Cartographica Sinica
