■葉序らせん(その93)
A(−bs,0,bc)
B(bs,0,bc)
C(0,h,0)
D(xc,y,xs)
E(−xc,y,−xs)
F(αc−γs,β,αs+γc)
G(ξc−ζs,η,ξs+ζc)
中心軸をO(X,Y,0)として,
OC=OA=OD(=OF)
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OC^2=X^2+(Y−h)^2
OA^2=(X+bs)^2+Y^2
OD^2=(X−xc)^2+(Y−y)^2
−2Yh+h^2−2Xbs−b^2s^2=0
2Xxc−x^2c^2−2Yh+h^2+2Yy−y^2=0
2Xbs+2Yh=h^2−b^2s^2
2Xxc+2Y(y−h)=x^2c^2−h^2+y^2
D=4bs(y−h)−4hxc
X={2(h^2−b^2s^2)(y−h)−2(x^2c^2−h^2+y^2)h}/D
Y={2bs(x^2c^2−h^2+y^2)−2xc(h^2−b^2s^2)}/D
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cos(∠AOC)=cos(∠AOD)(=cos(∠DOF))を求めればよい.
cos(∠AOC)={X(bs+X)−Y(h−Y)}/{(bs+X)^2+Y^2)^1/2・(X^2+(h−Y)^2)^1/2
cos(∠AOD)={−(bs+X)(xc−X)n−Y(y−Y)}/{(bs+X)^2+Y^2)^1/2・((xc−X)^2+(h−Y)^2)^1/2
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