球坐标系x=rsinθcosφy=rsinθsinφz=rcosθ{x=rsinθcosφy=rsinθsinφz=rcosθr∈[0,+∞),θ∈[0,π],φ∈[0,2π] 球坐标系 x=rsinθcosφ y=rsinθsinφ z=rcosθ\\ \left\{\begin{array}{l}x=r\sin\theta\cos\varphi\\y=r\sin\theta\sin\varphi\\z=r\cos\theta\end{array}\right. r∈[0,+∞),θ∈[0, π], φ∈[0,2π] 球坐标系x=rsinθcosφy=rsinθsinφz=rcosθ⎩⎨⎧x=rsinθcosφy=rsinθsinφz=rcosθr∈[0,+∞),θ∈[0,π],φ∈[0,2π]
弧长公式
L=n× π× r/180,L=α× r
弧长=弧度*半径
图片来源于网络
在球坐标系中,沿基矢方向的三个线段元为:{dlr=drdlφ=rsinθdφdlθ=rdθ球坐标的面元面积是:dS=dl(θ)∗dl(φ)=r2sinθdθdφ体积元的体积为:dV=dl(r)∗dl(θ)∗dl(φ)=r2sinθdrdθdφ
在球坐标系中,沿基矢方向的三个线段元为:
\\
\left\{\begin{array}{l}dl_r=dr\\dl_\varphi^{}=r\sin\theta d\varphi\\dl_\theta=rd\theta\end{array}\right.\\
球坐标的面元面积是:\\
dS=dl(θ)* dl(φ)=r2sinθdθdφ\\
体积元的体积为:\\
dV=dl(r)*dl(θ)*dl(φ)=r2sinθdrdθdφ
在球坐标系中,沿基矢方向的三个线段元为:⎩⎨⎧dlr=drdlφ=rsinθdφdlθ=rdθ球坐标的面元面积是:dS=dl(θ)∗dl(φ)=r2sinθdθdφ体积元的体积为:dV=dl(r)∗dl(θ)∗dl(φ)=r2sinθdrdθdφ
r=1
θ=1
φ=1
向量((0, 0, 0), ( r*sin(θ)sin(φ),0, 0))
向量((0, 0, 0), (0, r*sin(θ)sin(φ), 0))
向量((0, 0, 0), (0, 0, r*cos(θ)))
向量((0, 0, 0), ( r*sin(θ)sin(φ), r*sin(θ)sin(φ), r*cos(θ))))