1 弧长 arc length
如上图所示,设$\Delta S=S_i-S_{i-1}$
- 将弧长近似为线段,由此可得$(\Delta S)^2 \approx(\Delta x)^2+(\Delta y)^2$
- 无限细化$S_i$与$S_{i-1}$之间的距离,可得$(ds)^2 =(dx)^2+(dy)^2$
- 化简得$ds=\sqrt{1-(\frac{dy}{dx})^2}dx$
- 从$S_0$到$S_n$的总弧长$=\int_a
分类标签归档:参数方程
如上图所示,设$\Delta S=S_i-S_{i-1}$