ローテーション (回転)

rotation は回転．ベクトル量

$$\mathrm{rot} \bm{A} =\nabla\times\bm{A}$$

$$=\left(\bm{i}\frac{\partial}{\partial x}+\bm{j}\frac{\partial}{\p... ...+ \bm{k}\frac{\partial}{\partial z}\right)\times(A_x\bm{i}+A_y\bm{j}+A_z\bm{k})$$

$$=\left(\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\parti... ...ft(\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}\right)\bm{k}$$ (7.17)

行列式を使って

$$\mathrm{rot} \bm{A} =\begin{vmatrix}\partial/\partial y & \partial/\partial z \ A_y ... ...atrix}\partial/\partial x & \partial/\partial y \ A_x & A_y\end{vmatrix}\bm{k}$$

$$=\begin{vmatrix}\bm{i} & \bm{j} & \bm{k}\ \partial/\partial x & \partial/\partial y & \partial/\partial z\ A_x & A_y & A_z \end{vmatrix}$$ (7.18)

と書くと覚えやすい．