是否有办法来调整这个系统非线性方程 [英] Is there a way to adjust this system of non linear equation

问题描述

我已经解决了这个问题的最后2天，但没有成功。
说我们有这个制度：
    

I've been to solve this problem for the last 2 days with no success. say we have this system :

该解决方案具有的无限数量时：

the has an infinite number of solutions when :

获得Theta角度的价值，我用这个公式：

to get value of the angle Theta, I use this formula :

这是我得到的值是正确的，但只在某些点，因为该系统是不可解。
这里是它的样子：

The value that I get is correct but only in some points, because the system isn't solvable. and here is how it looks like :

红色曲线重新presents的必应的价值和蓝色的再presents我居然得到。

the red curve represents the "must be" value and the blue one represents that I actually get.

ploting总和的值后：

after ploting the value of the sum :

这里是我得到：

正如你可以看到它的正弦曲线，这似乎影响角度的必应的价值。

here is what I get : as you can see it's sinus curve, that seems to influence the "must be" value of the angle.

模拟这个我一直在使用这个程序：

to simulate this I've been using this program :

      #include <stdio.h>
#include <math.h>


int main (){
  float xin =0;
  float yin =0;
  float zin =0;
  float A =0;
  float B =0;
  float C =0;
  float angle =0;
  float outangle =0 ;
  float angledeg =0;
  while (angledeg <=(360*3)) {

    angle = angledeg * M_PI/180;
    xin = 0.11;
    yin = (sin(angle) / sqrt(3))  + xin;
    zin = (xin - (sin(angle +(120*M_PI/180))));
    A  = yin - xin;
    B  = xin - zin;
    C  = zin - yin;
    outangle = atan2((A*sqrt(3)) , (B -C) )   * 180/M_PI; // 100% correct 
    printf ("%lf \n" , outangle);
    angledeg++;
  }

  return 0;
}

所以我的问题是：我如何使用总和的值来调整的结果值必应的角度（红色曲线）的值

So my QUESTION is : how could I use the value of sum to adjust the resulted value of "must be" value of the angle ( the red curve)

更新

我不知道这是否使感，但它的工作原理：删除的sqrt（3）：

I don't know if this make a sense but it works : Removing sqrt(3) :

yin = (sin(angle) / sqrt(3))  + xin;

我真的不明白这一点，但它工作正常？任何想法，为什么？

I really don't get it, but it works fine ? any idea why ?

推荐答案

您可以极大地考虑简化局面

You can dramatically simplify the situation by considering that

sin(t)+sin(t+120°)+sin(t+240°)=0

这只是意味着在单位圆上的任何等边三角形的（重量）的中心点为原点

which just means that the (weight) center point of any equilateral triangle on the unit circle is the origin.

因此​​，

sin(t)/sqrt(3)+sin(t+120°)+sin(t+240°)=sin(t)*(1/sqrt(3)-1)

所以 T = THETA ，使系统可以解决的是 T = 0°和<$唯一值C $ C> T = 180°。

So the only values of t=theta that make the system solvable are t=0° and t=180°.

在计算

y=x+sin(t)/sqrt(3); z=x-sin(t+120°)

你生产作为对C值

you produce as value for C

z-y = - sin(t+120°) - sin(t)/sqrt(3)

和由此

B-C = 2*sin(t+120°) + sin(t)/sqrt(3)
    = -sin(t) + sqrt(3)*cos(t) + sin(t)/sqrt(3)

其中某种期待你只想到中期，这对于是真实的罪（T）= 0 ，再次为 T = 0°或 T = 180°。

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