正交坐标系下拉普拉斯算符的迭代推导  

Iterative Derivation of Laplace Operator in the Orthogonal Coordinate System

作　　者：丁波 欧志华[1] 奉瑞萍 DING Bo;OU Zhi-hua;FENG Rui-ping(School of Civil Engineering,Hunan University of Technology,Zhuzhou 412007,China)

机构地区：[1]湖南工业大学土木工程学院,湖南株洲412007

出　　处：《数学的实践与认识》2021年第17期222-227,共6页Mathematics in Practice and Theory

摘　　要：抛开以往用繁杂的复合函数链式求导法则来计算拉普拉斯算符在直角坐标系、柱坐标系和球坐标系中的表达式,通过建立一般的正交坐标系统来推导迭代拉普拉斯算符,从数量场的梯度计算到向量场的散度计算过程揭示了拉普拉斯算符的物理本质.Instead of using the past complex chain rule of composite function to calculate the expression of Laplace operator in rectangular coordinate system,cylindrical coordinate system and spherical coordinate system.In this paper,the iterative Laplace operator is derived by establishing a general orthogonal coordinate system.The physical essence of Laplace operator is revealed from the gradient calculation of scalar field to the divergence calculation of vector field.

关 键 词：坐标系统 梯度 散度 拉普拉斯算符 

分 类 号：O175.2[理学—数学]