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小木虫论坛-学术科研互动平台 » 计算模拟区 » 程序语言 » MATLAB/Mathematica » 求解非线性方程组
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七匹狼狗

木虫 (小有名气)

[求助] 求解非线性方程组 已有1人参与

新人，求了好久都求不出来
f=[f1;f2;f3];
f1=sin(x2 + q1 - x1)*cos(alpha1)*((cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*(2*c*x2*ipg1*sin(deltaf1) - ipg1*sin(deltaf1) + 1) + E1*ipg1*sin(deltaf1)*(2*c*x2 - 1)) - cos(x2 + q1 - x1)*cos(alpha1)*((S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)))*(2*c*x2*ipg1*sin(deltaf1) - ipg1*sin(deltaf1) + 1) + XB1*ipg1*cos(deltaf1)*(2*c*x2 - 1) + ipg1*x3*cos(alpha1)*cos(deltaf1)*(2*c*x2 - 1)) - ipg1*cos(deltaf1)*sin(alpha1)*(2*c*x2 - 1)*(E1 + rg1*cos(x2 + q1 - x1) - S1*sin(x2 + q1) + x3*cos(x2 + q1 - x1)*sin(alpha1)));
f2= Zp1 - X1*sin(deltaf1 + deltaf2) - Am1*cos(a1) - xp3*cos(a1) + yp3*sin(a1) - XB1*sin(deltaf1 + deltaf2)*sin(deltaf1) + E1*sin(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2) - x3*sin(deltaf1 + deltaf2)*cos(alpha1)*sin(deltaf1) - S1*sin(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*sin(x2 + q1) + XB1*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(deltaf1) + S1*cos(x2 + q1)*sin(deltaf1 + deltaf2)*cos(deltaf1) + rg1*sin(x2 + q1 - x1)*sin(deltaf1 + deltaf2)*cos(deltaf1) + rg1*sin(x2*ipg1*(c*x2 - 1))*cos(x2 + q1 - x1)*cos(deltaf1 + deltaf2) + x3*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(alpha1)*cos(deltaf1) + x3*sin(x2 + q1 - x1)*sin(deltaf1 + deltaf2)*cos(deltaf1)*sin(alpha1) + S1*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(x2 + q1)*sin(deltaf1) + x3*sin(x2*ipg1*(c*x2 - 1))*cos(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(alpha1) + rg1*cos(x2*ipg1*(c*x2 - 1))*sin(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(deltaf1) + x3*cos(x2*ipg1*(c*x2 - 1))*sin(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(alpha1)*sin(deltaf1);
f3=(abs(cos(deltaf1)*(cos(pi/2 - deltaf1 - deltaf2)*(sin(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) - sin(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))) + sin(pi/2 - deltaf1 - deltaf2)*(cos(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + sin(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1)) - cos(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))))) + sin(deltaf1)*(sin(pi/2 - deltaf1 - deltaf2)*(sin(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) - sin(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))) - cos(pi/2 - deltaf1 - deltaf2)*(cos(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + sin(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1)) - cos(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))))))^2 + abs(cos(deltaf1)*(sin(ipg1*(x2 - c*x2^2))*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*((E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*cos(deltaf1)^2 + (E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*sin(deltaf1)^2)))^2 + abs(sin(deltaf1)*(sin(ipg1*(x2 - c*x2^2))*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*((E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*cos(deltaf1)^2 + (E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*sin(deltaf1)^2)))^2)^(1/2) - Am1*sin(a1) - yp3*cos(a1) - xp3*sin(a1);
上式中：
rg1=110.440;
alpha1=roundn(19*pi/180,-6);
q1=roundn(69.4900*pi/180,-6);
ipg1=3.2953;
S1=101.7300;
deltaf1=roundn(16.1035*pi/180,-6);
deltaf2=roundn(69.0784*pi/180,-6);
XB1=0.5300;%此处的字母“b”多余，删除
X1=-1.9100;
E1=2.5400;
c=-0.000010;
a1=roundn(17.7*pi/180,-6);
Am1=roundn(37.5/sin(a1)-35/2,-6);
Zp1=0;
xp3=2.604843;
yp3=-1.324843;
求解[x1;x2;x3]
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1楼 2015-11-27 09:34:09
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月只蓝

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【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ...
感谢参与，应助指数 +1
七匹狼狗: 金币+500, ★★★很有帮助, 虽然没怎么看懂，也不知道结果对不对，但真能算出来，而且速度很快！ 2015-11-27 20:55:09
三角函数，应该有多组解，现求得x1，x2，x3=1附近的解，MATLAB代码如下：
CODE:
function solve_neqs
clear all;clc
format long
x0=[1 1 1];
[x fval]=fsolve(@n_eqs,x0);

[x ;fval]'


function f=n_eqs(u)
x1=u(1);
x2=u(2);
x3=u(3);

rg1=110.440;
alpha1=roundn(19*pi/180,-6);
q1=roundn(69.4900*pi/180,-6);
ipg1=3.2953;
S1=101.7300;
deltaf1=roundn(16.1035*pi/180,-6);
deltaf2=roundn(69.0784*pi/180,-6);
XB1=0.5300;%此处的字母“b”多余，删除
X1=-1.9100;
E1=2.5400;
c=-0.000010;
a1=roundn(17.7*pi/180,-6);
Am1=roundn(37.5/sin(a1)-35/2,-6);
Zp1=0;
xp3=2.604843;
yp3=-1.324843;

f1=sin(x2 + q1 - x1)*cos(alpha1)*((cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*(2*c*x2*ipg1*sin(deltaf1) - ipg1*sin(deltaf1) + 1) + E1*ipg1*sin(deltaf1)*(2*c*x2 - 1)) - cos(x2 + q1 - x1)*cos(alpha1)*((S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)))*(2*c*x2*ipg1*sin(deltaf1) - ipg1*sin(deltaf1) + 1) + XB1*ipg1*cos(deltaf1)*(2*c*x2 - 1) + ipg1*x3*cos(alpha1)*cos(deltaf1)*(2*c*x2 - 1)) - ipg1*cos(deltaf1)*sin(alpha1)*(2*c*x2 - 1)*(E1 + rg1*cos(x2 + q1 - x1) - S1*sin(x2 + q1) + x3*cos(x2 + q1 - x1)*sin(alpha1));
f2= Zp1 - X1*sin(deltaf1 + deltaf2) - Am1*cos(a1) - xp3*cos(a1) + yp3*sin(a1) - XB1*sin(deltaf1 + deltaf2)*sin(deltaf1) + E1*sin(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2) - x3*sin(deltaf1 + deltaf2)*cos(alpha1)*sin(deltaf1) - S1*sin(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*sin(x2 + q1) + XB1*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(deltaf1) + S1*cos(x2 + q1)*sin(deltaf1 + deltaf2)*cos(deltaf1) + rg1*sin(x2 + q1 - x1)*sin(deltaf1 + deltaf2)*cos(deltaf1) + rg1*sin(x2*ipg1*(c*x2 - 1))*cos(x2 + q1 - x1)*cos(deltaf1 + deltaf2) + x3*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(alpha1)*cos(deltaf1) + x3*sin(x2 + q1 - x1)*sin(deltaf1 + deltaf2)*cos(deltaf1)*sin(alpha1) + S1*cos(x2*ipg1*(c*x2 - 1))*cos(deltaf1 + deltaf2)*cos(x2 + q1)*sin(deltaf1) + x3*sin(x2*ipg1*(c*x2 - 1))*cos(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(alpha1) + rg1*cos(x2*ipg1*(c*x2 - 1))*sin(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(deltaf1) + x3*cos(x2*ipg1*(c*x2 - 1))*sin(x2 + q1 - x1)*cos(deltaf1 + deltaf2)*sin(alpha1)*sin(deltaf1);
f3=(abs(cos(deltaf1)*(cos(pi/2 - deltaf1 - deltaf2)*(sin(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) - sin(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))) + sin(pi/2 - deltaf1 - deltaf2)*(cos(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + sin(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1)) - cos(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))))) + sin(deltaf1)*(sin(pi/2 - deltaf1 - deltaf2)*(sin(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) - sin(ipg1*(x2 - c*x2^2))*cos(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))) - cos(pi/2 - deltaf1 - deltaf2)*(cos(deltaf1)*(sin(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) - cos(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + sin(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1)) - cos(ipg1*(x2 - c*x2^2))*sin(deltaf1)*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))))))^2 + abs(cos(deltaf1)*(sin(ipg1*(x2 - c*x2^2))*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*((E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*cos(deltaf1)^2 + (E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*sin(deltaf1)^2)))^2 + abs(sin(deltaf1)*(sin(ipg1*(x2 - c*x2^2))*(cos(deltaf1)*(XB1 + X1*sin(deltaf1) + x3*cos(alpha1)) + sin(deltaf1)*(S1*cos(x2 + q1) + sin(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - X1*cos(deltaf1))) + cos(ipg1*(x2 - c*x2^2))*((E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*cos(deltaf1)^2 + (E1 + cos(x2 + q1 - x1)*(rg1 + x3*sin(alpha1)) - S1*sin(x2 + q1))*sin(deltaf1)^2)))^2)^(1/2) - Am1*sin(a1) - yp3*cos(a1) - xp3*sin(a1);

f=[f1 f2 f3];

上述代码完全复制进一个新建的m文件中，运行即可。
计算结果：
          x1~x3                     方程残差
   0.540342687064503  -0.000000000000043
   0.076269763905084  -0.000000000000014
   9.546938126545205   0.000000000000013
求解非线性方程组
附图.png
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2楼2015-11-27 11:19:24
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七匹狼狗

木虫 (小有名气)
引用回帖:
2楼: Originally posted by 月只蓝 at 2015-11-27 11:19:24
三角函数，应该有多组解，现求得x1，x2，x3=1附近的解，MATLAB代码如下：
function solve_neqs
clear all;clc
format long
x0=;
=fsolve(@n_eqs,x0);

'


function f=n_eqs(u)
x1=u(1);
x2=u(2);
x3= ...

谢谢~
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3楼2015-11-27 20:53:47
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月只蓝

主管区长 (职业作家)
引用回帖:
3楼: Originally posted by 七匹狼狗 at 2015-11-27 20:53:47
谢谢~...

结果对不对看方程残差就知道了。
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4楼2015-11-28 07:03:20
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