カテゴリー: ベクトル解析

\[ \boldsymbol{\nabla}\cdot\boldsymbol{A}=\frac{1}{h}\sum_{i}\frac{\partial}{\partial q_{i}}\frac{A_{i}h}{h_{i}} \]

\[ \boldsymbol{\nabla}\cdot\boldsymbol{u}_{i}=\frac{1}{hh_{i}}\frac{\partial}{\partial q_{i}}h-\frac{1}{h_{i}^{2}}\frac{\partial}{\partial q_{i}}h_{i} \]

\[ h_{i}\boldsymbol{\nabla}q_{i}=\frac{1}{h_{i}}\frac{\partial\boldsymbol{r}}{\partial q_{i}} \]

\[ \boldsymbol{u}_{i}=\frac{1}{h_{i}}\frac{\partial\boldsymbol{r}}{\partial q_{i}} \]

\[ \nabla_{\boldsymbol{v}}f\left(\boldsymbol{r}\right):=\boldsymbol{v}\cdot\boldsymbol{\nabla}f \]

\[ \iiint_{V}\boldsymbol{\nabla}\cdot\boldsymbol{A}dV=\iint_{S}\boldsymbol{A}\cdot d\boldsymbol{S} \]

\[ \boldsymbol{\nabla}:=\boldsymbol{e}_{i}\partial_{i} \]