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旋度 - Wikipedia

旋度

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[编辑] 定义

设有向量场

\mathbf{A}(x,y,z)=P(x,y,z)\mathbf{i}+Q(x,y,z)\mathbf{j}+R(x,y,z)\mathbf{k}，

在坐标上的投影分别为

\frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z}，\frac{\partial P}{\partial z}-\frac{\partial R}{\partial x}，\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}

的向量叫做向量场A的旋度，记作 rot A，即

\mathbf{rot}\ \mathbf{A}=(\frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z})\mathbf{i}+(\frac{\partial P}{\partial z}-\frac{\partial R}{\partial x})\mathbf{j}+(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y})\mathbf{k}

[编辑] 行列式记号

旋度rot A的表达式可以用含列式记号形式表示：

\mathbf{rot}\ \mathbf{A}=\begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac {\partial}{\partial z} \\ P & Q & R \end{vmatrix}

[编辑] 含义

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