求交点

xkitty

已知对数螺线方程: x= a1 * Exp(m0 * β) * Cos(β)
y= a1 * Exp(m0 * β) * Sin(β) 直线方程：y=kx+b 其中，a1、m0、k、b均为已知常数。如何求两曲线的交点？请大家指点迷津。

雪山飞狐_lzh

纯数学方法求解（不过上学没用功，忘光了）

ahlzl

这个方程是“解不出来”的……用VBA试试！

2. Sub abc()a1 = 4: m0 = 1: k = 1: b = -3     '一个例子
3. Dim z0 As Double, z1 As Double
4. z0 = 0     '赋初值
5. z1 = z0
6. Do
7. z0 = z1
8. fz = a1 * Exp(m * z0) * Sin(z0) - a1 * Exp(m * z0) * Cos(z0) - b
9. flz = a1 * Exp(m * z0) * Cos(z0) + a1 * m * Exp(m * z0) * Cos(z0) _
10. - a1 * m * Exp(m * z0) * Cos(z0) + a1 * Exp(m * z0) * Sin(z0)z1 = z0 - fz / flz
11. Loop While Abs(z1 - z0) > 0.000000001x = a1 * Exp(z0) * Cos(z0)
12. y = a1 * Exp(z0) * Sin(z0)
13. MsgBox "z0=" & z0 & "时" & vbCrLf & vbCrLf & "x=" & x & vbCrLf & "y=" & yEnd Sub

Sub abc()a1 = 4: m0 = 1: k = 1: b = -3     '一个例子 Dim z0 As Double, z1 As Double z0 = 0     '赋初值 z1 = z0 Do z0 = z1 fz = a1 * Exp(m * z0) * Sin(z0) - a1 * Exp(m * z0) * Cos(z0) - b flz = a1 * Exp(m * z0) * Cos(z0) + a1 * m * Exp(m * z0) * Cos(z0) _ - a1 * m * Exp(m * z0) * Cos(z0) + a1 * Exp(m * z0) * Sin(z0)z1 = z0 - fz / flz Loop While Abs(z1 - z0) > 0.000000001x = a1 * Exp(z0) * Cos(z0) y = a1 * Exp(z0) * Sin(z0) MsgBox "z0=" & z0 & "时" & vbCrLf & vbCrLf & "x=" & x & vbCrLf & "y=" & yEnd Sub

另，这个交点可是有无穷多个啊！这个例子只是求出一个。(代码中的z0就是β)

xkitty

斑竹数学真棒！唉，我怎末没想起来用迭代法计算，计算方法真是白学了！多谢斑竹老师的指点！“长不大的斑竹”太伟大了！