\Delta S_{\mathbf{n}}代表以单位向量\vec n为法向量的面元，\Gamma_{\mathbf{n}}是\Delta S_...
\int_{\partial S}{\vec{F}\,\,·\,\,d\vec{r}=}\int_{\partial R}{\begin{array}{c} \left( G_1ds+G_2dt \right) \,\,\\ \end{array}} \\ Use Green's Theorem, we know \int_{\partial R}{\begin{array}{c} \left( G_1ds+G_2dt \right)\\ \end{array}}=\int_R{\be...
要记住斯托克斯公式，首要的是理解其背后的含义和符号的含义。斯托克斯公式在向量积分学中，是一个非常关键的定理。它将曲面积分转换为围绕闭合路径的线积分，体现了场的旋转与线积分之间的关系。斯托克斯公式的数学表达为：∫∫_S ∇ × F · dS = ∮_C F · dr，其中 S 是闭合曲面，C 是...
斯托克斯沉速公式定理：公式如下：w=【2(ρS－ρ)gr2】/9μ式中：ρS为颗粒密度；ρ为水的密度；μ为流体黏度；r为颗粒半径；g为重力加速度。此公式是在静水、20℃恒温、介质的黏度不变、球形颗粒、密度相同、表面光滑、颗粒互不碰撞的实验室理想条件下获得的。当然与自然界的实际情况相差很大，因...
网络左式到右式是透过;斯托克司定理;斯托克斯定理 网络释义
In this special case, Stokes’ theorem gives ∫CF⋅dr=∬Scurl F⋅kdA∫CF⋅dr=∬Scurl F⋅kdA. However, this is the circulation form of Green’s theorem, which shows us that Green’s theorem is a special case of Stokes’ theorem. Green’s theorem can only handle surfaces in ...
Stokes’Theorem Adding circulations Consider two rectangular loops that share a common edge as shown below. Let C1 be the blue loop and C2 be the red loop with orientations as shown. Let C3 be the loop that consists of going around the outside of the large rectangle formed by removing the...
Math 21a Stokes’ Theorem Spring, 2009´&$%Cast of Players:S – an oriented, piecewise-smooth surfaceC – a simple, closed, piecewise-smoot..