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柱面坐标系中的体积元素

2009-08-11 21:40:50| 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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高等数学图形与动画

柱面坐标系中的体积元素

在利用柱面坐标计算三重积分时，我们用柱面坐标的三组坐标面去划分一个空间区域，得到一个典型的体积元素，其图形如下：

with(plots):
banpingmian1:=plot3d([r,Pi/6,z],r=1..2,z=1..1.5,coords=cylindrical,color=green):
banpingmian2:=plot3d([r,Pi/3,z],r=1..2,z=1..1.5,coords=cylindrical,color=green):
banpingmian3:=plot3d([r,Pi/6,z],r=0..2.2,z=0.8..1.8,coords=cylindrical,color=green,style=wireframe):
banpingmian4:=plot3d([r,Pi/3,z],r=0..2.2,z=0.8..1.8,coords=cylindrical,color=green,style=wireframe):
zhumian1:=plot3d([1,theta,z],theta=Pi/6..Pi/3,z=1..1.5,coords=cylindrical,color=red):
zhumian2:=plot3d([2,theta,z],theta=Pi/6..Pi/3,z=1..1.5,coords=cylindrical,color=red):
zhumian3:=plot3d([1,theta,z],theta=0..Pi/2,z=0.8..1.8,coords=cylindrical,color=red,style=wireframe):
zhumian4:=plot3d([2,theta,z],theta=0..Pi/2,z=0.8..1.8,coords=cylindrical,color=red,style=wireframe):
pingmian1:=plot3d([r,theta,1],r=1..2,theta=Pi/6..Pi/3,coords=cylindrical,color=blue):
pingmian2:=plot3d([r,theta,1.5],r=1..2,theta=Pi/6..Pi/3,coords=cylindrical,color=blue):
pingmian3:=plot3d([r,theta,1],r=0..2.3,theta=0..Pi/2,coords=cylindrical,color=blue,style=wireframe):
pingmian4:=plot3d([r,theta,1.5],r=0..2.3,theta=0..Pi/2,coords=cylindrical,color=blue,style=wireframe):
P:=display(banpingmian1,banpingmian2,banpingmian3,banpingmian4,zhumian1,zhumian2,zhumian3,zhumian4,pingmian1,pingmian2,pingmian3,pingmian4,style=patchnogrid):
x_axis:=plot3d([u,0,0],u=-1.5..1.5,v=0..0.01):
y_axis:=plot3d([0,u,0],u=-1.5..1.5,v=0..0.01):
z_axis:=plot3d([0,0,u],u=-0.5..2,v=0..0.01):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(P,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4]);

with(plots):
banpingmian1:=plot3d([r,Pi/6,z],r=1..2,z=1..1.5,coords=cylindrical,color=green):
banpingmian2:=plot3d([r,Pi/3,z],r=1..2,z=1..1.5,coords=cylindrical,color=green):
zhumian1:=plot3d([1,theta,z],theta=Pi/6..Pi/3,z=1..1.5,coords=cylindrical,color=red):
zhumian2:=plot3d([2,theta,z],theta=Pi/6..Pi/3,z=1..1.5,coords=cylindrical,color=red):
pingmian1:=plot3d([r,theta,1],r=1..2,theta=Pi/6..Pi/3,coords=cylindrical,color=blue):
pingmian2:=plot3d([r,theta,1.5],r=1..2,theta=Pi/6..Pi/3,coords=cylindrical,color=blue):
K:=30:for i from 1 to K do ti:=i*360/K:
p[i]:=display(banpingmian1,banpingmian2,zhumian1,zhumian2,pingmian1,pingmian2,
orientation=[ti,60],style=patchnogrid):od:
P:=display([seq(p[i],i=1..K)],insequence=true):
x_axis:=plot3d([u,0,0],u=-1.5..1.5,v=0..0.01):
y_axis:=plot3d([0,u,0],u=-1.5..1.5,v=0..0.01):
z_axis:=plot3d([0,0,u],u=-0.5..2.5,v=0..0.01):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(P,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4]);

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              blogAbstract:'<P align=left\><A href=\"http://xuxzmail.blog.163.com/blog/static/251319162009614101444586/\" target=_blank\>高等数学图形与动画</A\></P\>\r\n<P\><FONT size=3\></FONT\> </P\>\r\n<P\><FONT face=楷体_GB2312 size=3\><STRONG\>柱面坐标系中的体积元素</STRONG\></FONT\></P\>\r\n<P\><FONT size=3\>在利用柱面坐标计算三重积分时，我们用</FONT\><A href=\"http://xuxzmail.blog.163.com/blog/static/251319162009222102552106/\" target=_blank\><FONT size=3\>柱面坐标的三组坐标面</FONT\></A\><FONT size=3\>去划分一个空间区域，得到一个典型的体积元素，其图形如下：</FONT\></P\>\r\n<P\><A href=\"http://img.bimg.126.net/photo/34OhPTDJBCJce-3dufMphA==/4230005950008369329.jpg\" target=_blank\><IMG title=\"柱面坐标系中的体积元素 - Calculus - 高等数学\" alt=\"柱面坐标系中的体积元素 - Calculus - 高等数学\" src=\"http://img.bimg.126.net/photo/34OhPTDJBCJce-3dufMphA==/4230005950008369329.jpg\"\></A\><BR\><BR\>with(plots):<BR\>banpingmian1:=plot3d([r,Pi/6,z],r=1..2,z=1..1.5,coords=cylindrical,color=green):</P\>',
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