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球面坐标系中的体积元素

2009-08-11 21:58:47| 分类：高等数学图形动画 | 标签： |举报 |字号大中小订阅

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所有图形见：高等数学图形与动画

球面坐标系中的体积元素

在利用球面坐标计算三重积分时，我们用球面坐标的三组坐标面去划分一个空间区域，得到的一个典型的体积元素形如下图：

with(plots):
banpingmian1:=plot3d([r,Pi/5,phi],r=1..1.5,phi=Pi/5..Pi/3,coords=spherical,color=green):
banpingmian2:=plot3d([r,Pi/3,phi],r=1..1.5,phi=Pi/5..Pi/3,coords=spherical,color=green):
zuimian1:=plot3d([r,theta,Pi/5],theta=Pi/5..Pi/3,r=1..1.5,coords=spherical,color=yellow):
zuimian2:=plot3d([r,theta,Pi/3],theta=Pi/5..Pi/3,r=1..1.5,coords=spherical,color=yellow):
qiumian1:=plot3d([1,theta,phi],phi=Pi/5..Pi/3,theta=Pi/5..Pi/3,coords=spherical,color=red):
qiumian2:=plot3d([1.5,theta,phi],phi=Pi/5..Pi/3,theta=Pi/5..Pi/3,coords=spherical,color=red):
P:=display(banpingmian1,banpingmian2,zuimian1,zuimian2,qiumian1,qiumian2,orientation=[15,70],style=patchnogrid):
display(P,lightmodel=light2);

with(plots):
banpingmian1:=plot3d([r,Pi/5,phi],r=1..1.5,phi=Pi/5..Pi/3,coords=spherical,color=green):
banpingmian2:=plot3d([r,Pi/3,phi],r=1..1.5,phi=Pi/5..Pi/3,coords=spherical,color=green):
zuimian1:=plot3d([r,theta,Pi/5],theta=Pi/5..Pi/3,r=1..1.5,coords=spherical,color=yellow):
zuimian2:=plot3d([r,theta,Pi/3],theta=Pi/5..Pi/3,r=1..1.5,coords=spherical,color=yellow):
qiumian1:=plot3d([1,theta,phi],phi=Pi/5..Pi/3,theta=Pi/5..Pi/3,coords=spherical,color=red):
qiumian2:=plot3d([1.5,theta,phi],phi=Pi/5..Pi/3,theta=Pi/5..Pi/3,coords=spherical,color=red):
K:=30:for i from 1 to K do ti:=i*360/K:
p[i]:=display(banpingmian1,banpingmian2,zuimian1,zuimian2,qiumian1,qiumian2,orientation=[ti,60],style=patchnogrid) od:
P:=display([seq(p[i],i=1..K)],insequence=true):
display(P,lightmodel=light2);

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