仿射空间拉普拉斯算子探讨  

Discussion of Laplace operator in affine space

作　　者：张捍卫[1] 李晓玲 杨永勤 张华 ZHANG Hanwei;LI Xiaoling;YANG Yongqin;ZHANG Hua(School of Surveying and Land Information Engineering,Henan Polytechnic University,Jiaozuo,Henan 454003,China)

机构地区：[1]河南理工大学测绘与国土信息工程学院,河南焦作454003

出　　处：《导航定位学报》2023年第1期48-52,共5页Journal of Navigation and Positioning

基　　金：国家自然科学基金项目(42074002,41931075)。

摘　　要：为了进一步研究提升惯性导航系统的精度,对拉普拉斯算子进行讨论:拉普拉斯算子是个微分算子,拉普拉斯方程又名调和方程、位势方程,求解拉普拉斯方程是物理学和力学等领域经常遇到的一类重要数学问题;基于曲线坐标系和张量理论,分别给出n维仿射空间中的拉普拉斯算子表达式,并证明不同表述的等价性;最后,基于格林定理和变方方法,分别给出3维仿射空间拉普拉斯算子的表达式。In order to further improve the accuracy of inertial navigation system,the Laplace operator was discussed:the Laplace operator is a differential operator,and Laplace’s equation,also known as harmonic equation,or potential equation;solving Laplace’s equation is an important mathematical problem in physics and mechanics;based on curvilinear coordinate system and tensor theory,the expressions of Laplacian operator in n-dimensional affine space were given respectively,and the equivalence of different expressions was proved;finally,based on Green’s theorem and variation method,expressions of Laplacian operator in 3-dimensional affine space were given respectively.

关 键 词：拉普拉斯算子 拉普拉斯方程 曲线坐标 格林定理 变分原理 

分 类 号：P228[天文地球—大地测量学与测量工程]