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| 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 |
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| DOI： |
| 中文关键词: 正交曲线坐标系 基向量 二阶偏导数 求导顺序 拉梅系数 |
| 英文关键词: orthogonal curvilinear coordinate system base vector second order partial derivative order of derivation Lame coef-ficient |
| 基金项目:复旦大学曦源项目，江苏省高等教育教学改革研究课题重点项目 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| The second order partial derivatives of base vectors in orthogonal curvilinear coordinate system are studied in this paper. 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 assertion 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. |
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