■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)

===================================

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

===================================

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

===================================