分針繞時針針尖旋轉(zhuǎn)時分針針尖的軌跡

1、分針繞時針針尖旋轉(zhuǎn)時，分針針尖的軌跡成都熊貓基地 06APR12一位網(wǎng)友提出以下問題： 機(jī)械鐘的時針和分針，都是圍繞鐘的中心軸順時針旋轉(zhuǎn)的。如果我們以時針的針尖為參考系，那么分針的針尖圍繞時針的針尖運(yùn)動軌道，是不是外擺線？設(shè)時針的長為 a，分針的長為 b。當(dāng)時針繞原點(diǎn)旋轉(zhuǎn)時，時針針尖的位置為：當(dāng)分針繞原點(diǎn)旋轉(zhuǎn)時，分針針尖的位置為：當(dāng)分針繞時針針尖旋轉(zhuǎn)時，分針針尖的位置為：所以，分針針尖的參數(shù)方程為：作圖的Maple程序：with(plots):a:=1:b:=1.2:k:=60:x:=t-a*cos(-t)+b*cos(-k*t);y:=t-a*sin(-t)+b*sin(-k*t);curv

2、e:=plot(x(t),y(t),t=0.2*Pi,thickness=2):display(curve,scaling=constrained,tickmarks=4,4);a=1, b=1.2 的圖形a=1, b=0.2 的圖形a=1, b=0.1 的圖形動畫1with(plots):a:=1:b:=1.2:k:=60:x:=t-a*cos(-t)+b*cos(-k*t);y:=t-a*sin(-t)+b*sin(-k*t);K:=180:for i from 1 to K doti:=i*0.5*Pi/K:quxiani:=plot(x(t),y(t),t=0.ti,thickness

3、=2):shizheni:=plot(0,0,a*cos(-ti),a*sin(-ti),color=blue,thickness=3):fenzheni:=plot(x(ti),y(ti),a*cos(-ti),a*sin(-ti),color=gray,thickness=3) od:quxian:=display(seq(quxiani,i=1.K),insequence=true):shizhen:=display(seq(shizheni,i=1.K),insequence=true):fenzhen:=display(seq(fenzheni,i=1.K),insequence=t

4、rue):display(quxian,shizhen,fenzhen,scaling=constrained,tickmarks=5,3);動畫2with(plots):a:=1:b:=0.2:k:=60:x:=t-a*cos(-t)+b*cos(-k*t);y:=t-a*sin(-t)+b*sin(-k*t);K:=360:for i from 1 to K doti:=i*1*Pi/K:quxiani:=plot(x(t),y(t),t=0.ti,thickness=2):shizheni:=plot(0,0,a*cos(-ti),a*sin(-ti),color=blue,thickn

5、ess=3):fenzheni:=plot(x(ti),y(ti),a*cos(-ti),a*sin(-ti),color=gray,thickness=3) od:quxian:=display(seq(quxiani,i=1.K),insequence=true):shizhen:=display(seq(shizheni,i=1.K),insequence=true):fenzhen:=display(seq(fenzheni,i=1.K),insequence=true):display(quxian,shizhen,fenzhen,scaling=constrained,tickma

6、rks=5,3);動畫3with(plots):a:=1:b:=0.1:k:=60:x:=t-a*cos(-t+Pi/2)+b*cos(-k*t+Pi/2);y:=t-a*sin(-t+Pi/2)+b*sin(-k*t+Pi/2);K:=360:for i from 1 to K doti:=i*2*Pi/K:quxiani:=plot(x(t),y(t),t=0.ti,thickness=2):shizheni:=plot(0,0,a*cos(-ti+Pi/2),a*sin(-ti+Pi/2),color=blue,thickness=3):fenzheni:=plot(x(ti),y(ti),a*cos(-ti+Pi/2),a*sin(-ti+Pi/2),color=gray,thickness=3) od:quxian:=display(seq(quxiani,i=1.K),insequence=true):shizhen:=display(seq(shizheni,i=1.K),insequence=true):fenzhen:=display