正交曲线坐标系基向量的二阶偏导数

The Second Order Partial Deaivatives of Base Vectors in Orthogonal Cuavilinear Coordinate System

研究了正交曲线坐标系基向量的二阶偏导数,运用基变换的单位正交性给出了当坐标函数三阶偏导数连续时拉梅系数满足的两个偏微分方程,由此证明了基向量的二阶混合偏导数与求导顺序无关,推导了基向量的二阶偏导数公式。

The second order partial derivatives of base vectors in orthogonal curvilinear coordinate system are studied in this pa per. Two partial differential equations in which the Lame coefficients satisfied under the circumstances that the third order partial derivatives of the coordinate functions continuous are given by using the unit orthogonality of the change of base. Thus the asser tion that the second order mixed partial derivatives are independence with the derivation order are demonstrated. The second order partial derivative formulas of base vectors are pushed out.