分針繞時針針尖旋轉(zhuǎn)時，分針針尖的軌跡

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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);c

2、urve:=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:forifrom1toKdoti:=i*0.5*Pi/K:quxian[i]:=plot([x(t),y(t),t=0..ti],t

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

4、y(seq(fenzhen[i],i=1..K),insequence=true):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:forifrom1toKdoti:=i*1*Pi/K:quxian[i]:=plot([x(t),y(t),t=0..ti],thickness=2):shizhen[i]:=p

5、lot([[0,0],[a*cos(-ti),a*sin(-ti)]],color=blue,thickness=3):fenzhen[i]:=plot([[x(ti),y(ti)],[a*cos(-ti),a*sin(-ti)]],color=gray,thickness=3)od:quxian:=display(seq(quxian[i],i=1..K),insequence=true):shizhen:=display(seq(shizhen[i],i=1..K),insequence=true):fenzhen:=display(seq(fenzhen[i],i=1..K),

6、insequence=true):display(quxian,shizhen,fenzhen,scaling=constrained,tickmarks=[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:forifrom1toKdoti:=i*2*Pi/K:quxian[i]:=plot([x(t),y(t),t=0..ti],thickness=2):shizhen[i]:=plot([

7、[0,0],[a*cos(-ti+Pi/2),a*sin(-ti+Pi/2)]],color=blue,thickness=3):fenzhen[i]:=plot([[x(ti),y(ti)],[a*cos(-ti+Pi/2),a*sin(-ti+Pi/2)]],color=gray,thickness=3)od:quxian:=display(seq(quxian[i],i=1..K),insequence=true):shizhen:=display(