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旋轮线

2009-08-02 21:44:26| 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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旋轮线（Cycloid）也叫摆线。一个半径为 a 的圆在x轴上滚动时，圆上一个点的轨迹就是旋轮线。

旋轮线 - calculus - 徐小湛的博客

旋轮线的参数方程是

其中theta是圆所转的角度。

参数方程的推导：

旋轮线的图形是（一拱）：

with(plots):a:=1:
curve:=plot([a*(theta-sin(theta)),a*(1-cos(theta)),theta=0..2*Pi],thickness=2):
display(curve,scaling=constrained,tickmarks=[0,0]);

两拱：

旋轮线 - calculus - 徐小湛的博客
with(plots):a:=1:
curve:=plot([a*(theta-sin(theta)),a*(1-cos(theta)),theta=0..4*Pi],thickness=2):
display(curve,scaling=constrained,tickmarks=[0,0]);

动画：

动画的Maple程序：

with(plots): with(plottools):
R:=1:a:=0:b:=4*Pi:
x:=t->R*(t-sin(t)):y:=t->R*(1-cos(t)):
K:=60:for i from 1 to K do ti:=a+i*(b-a)/K:
quxian[i]:=plot([x(t),y(t),t=a..ti]):
yuan[i]:=circle([ti,R],R,color=blue):
xian[i]:=plot([[ti,R],[x(ti),y(ti)]],color=brown):
M[i]:=display(quxian[i],yuan[i],xian[i]) od:
L:=display(seq(M[i],i=1..K),insequence=true):
display(L,L,scaling=constrained,tickmarks=[5,2],thickness=2);

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