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莫比乌斯带

2009-03-16 18:54:03| 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：数学图形目录

质点 P 在平面 z=0 上绕着点原点作角速度为 w1 的圆周运动（半径为 R），

同时，长为 2r 的直线又在z轴和P决定的平面上绕着 P 作角速度为 w2 的圆周运动（P 是直线的中点）。

求直线的运动轨迹的参数方程。

曲面的参数方程：

X=(R+s*cos((w2/w1)*theta))*cos(theta)

Y=(R+s*sin((w2/w1)*theta))*sin(theta)

Z=s*sin((w2/w1)*theta) (theta=0..2*Pi,s=-r..r)

当 w1=2*w2 时，曲面为莫比乌斯带（著名的单侧曲面）：

请看莫比乌斯带的形成过程：

w1=w2 时的图形：

莫比乌斯带 - Calculus - 高等数学

最后这个图形是用数学软件Mathematica绘制的。Mathematica程序：

A=ParametricPlot3D[{(1+v/2*Cos[1/2*u])*Cos[u],(1+v/2*Cos[1/2*u])*Sin[u],v/2*Sin[u/2]},{u,0,2*Pi},{v,-0.81,0.81},Boxed->False,Axes->None,PlotStyle->FaceForm[LightBlue,LightCyan],Mesh->{15,2}];
v=0.8;
B=ParametricPlot3D[{(1+v/2*Cos[1/2*u])*Cos[u],(1+v/2*Cos[1/2*u])*Sin[u],v/2*Sin[u/2]},{u,0,4*Pi},Boxed->False,Axes->None,PlotStyle->{Black,AbsoluteThickness[2]}];
Show[A,B]

返回：数学图形目录

Updated 13 JULY 2010

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