求助：怎么用matlab求解联立方程组啊

zhj

求助：急用：我想用matlab求解两个方程p1和Mcr，这两个方程里含有两个未知数x和gama，其他都是已知的值。我用了solve，可是结果总是显示empty空值，不知道是什么原因。望高手们能给以指点啊，我附上源程序，希望帮我解决一下这个问题了！谢谢了！
这里面的两个方程就是p1和Mcr让它们为零就可以了。

1. clc;clear;
   
2. syms gama ftk x
   
3. %x=685.2076;
   
4. %gama=1.0;
   
5. N=1600000; As=763; As1=66; b=115; hw=1000;
   
6. %Mcr=6E8;
   
7. Es=200000; Ec=38000; ftk=4.42; epsilontu=120.2E-6;
   
8. %ftk=Ec*epsilontu/gama;
   
9. phy=epsilontu/(hw-x);
   
10. as=((990-x)*339*10+(930-x)*226*70+(870-x)*66*130+(810-x)*66*190+(750-x)*66*250)/((990-x)*339+(930-x)*226+(870-x)*66+(810-x)*66+(750-x)*66)
    
11. epsilons=(hw-as-x)*phy; epsilons1=(650-x)*phy;
    
12. sigmas=Es*phy*(hw-as-x); sigmas1=epsilons1*Es;
    
13. Tc=0.5*gama*ftk*(hw-x)*b, Ts=Es*phy*(hw-as-x)*As, Ts1=sigmas1*As1
    
14. asp=as;
    
15. Asp=763; As1p=66; As2p=66; As3p=66;
    
16. epsilonsp=(x-asp)*phy; epsilons1p=phy*(x-350); epsilons2p=phy*(x-450); epsilons3p=phy*(x-550);
    
17. sigmasp=epsilonsp*Es; sigmas1p=Es*epsilons1p; sigmas2p=Es*epsilons2p; sigmas3p=Es*epsilons3p;
    
18. Tsp=(x-asp)*phy*Asp*Es, Cc=x*x*gama*ftk/(2*(hw-x))*b
    
19. Ts1p=sigmas1p*As1p, Ts2p=sigmas2p*As2p, Ts3p=sigmas3p*As3p
    
20. 
    
21. %p1=N+Tc+Ts-Tsp-Cc
    
22. p1=N+Tc+Ts+Ts1-Tsp-Cc-Ts1p-Ts2p-Ts3p
    
23. %p1=1600000+7.072*(1000-x)+(1.346e8*(1000-as-x)+13200000*(650-x)-134600000*(x-asp)-13200000*(x-350)-13200000*(x-450)-13200000*(x-550))*120.2e-6/(1000-x)-7.072*x^2/(1000-x)
    
24. %solve('N+Tc+Ts+Ts1-Tsp-Cc-Ts1p-Ts2p-Ts3p=0','x')
    
25. Mcr=Ts*(hw/2-as)+Tc*(hw/2-(hw-x)/3)+Ts1*150-Ts1p*50+Ts2p*50+Ts3p*150+Tsp*(hw/2-asp)+Cc*(hw/2-x/3)

复制代码

[ 本帖最后由 ChaChing 于 2009-8-14 23:01 编辑 ]

ChaChing

原帖由 zhj 于 2009-8-14 22:34 发表

                               
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...两个方程p1和Mcr，这两个方程里含有两个未知数x和gama，其他都是已知的值。我用了solve...

时间有限, 无法细看LZ的程序! sorry
两个方程两个未知数, 不就是典型的Ax=b ?
为何一定要用symbolic不能用数值解吗?  ==> x=A\b

zhj

主要是那两个方程里面同时含有x和gama两个变量，很长的式子。我没办法把它化简成那种很明显的形式。
p1=(14291182625542246875*(x - 350))/(9007199254740992*(x - 1000)) + (14291182625542246875*(x - 450))/(9007199254740992*(x - 1000)) + (14291182625542246875*(x - 550))/(9007199254740992*(x - 1000)) + (14291182625542246875*(x - 650))/(9007199254740992*(x - 1000)) + (330429464948143465625*(x - (56830*x - 48065700)/(763*x - 706170)))/(18014398509481984*(x - 1000)) + (330429464948143465625*(x + (56830*x - 48065700)/(763*x - 706170) - 1000))/(18014398509481984*(x - 1000)) - (5083*gama*(x - 1000))/20 + (5083*gama*x^2)/(10*(2*x - 2000)) + 1600000
Mcr=(357279565638556171875*(x - 350))/(4503599627370496*(x - 1000)) - (357279565638556171875*(x - 450))/(4503599627370496*(x - 1000)) - (1071838696915668515625*(x - 550))/(4503599627370496*(x - 1000)) + (1071838696915668515625*(x - 650))/(4503599627370496*(x - 1000)) + (330429464948143465625*(x - (56830*x - 48065700)/(763*x - 706170))*((56830*x - 48065700)/(763*x - 706170) - 500))/(18014398509481984*(x - 1000)) - (330429464948143465625*((56830*x - 48065700)/(763*x - 706170) - 500)*(x + (56830*x - 48065700)/(763*x - 706170) - 1000))/(18014398509481984*(x - 1000)) - (5083*gama*(x/3 + 500/3)*(x - 1000))/20 + (5083*gama*x^2*(x/3 - 500))/(10*(2*x - 2000))
这是最后的两个方程。怎么解啊？

ChaChing

[gamaSol,xSol]=solve(p1,Mcr,'x','gama')

friendchj

1. clc
   
2. clear
   
3. syms x gama
   
4. p1=(14291182625542246875*(x - 350))/(9007199254740992*(x - 1000)) + ...
   
5. (14291182625542246875*(x - 450))/(9007199254740992*(x - 1000)) + ...
   
6. (14291182625542246875*(x - 550))/(9007199254740992*(x - 1000)) + ...
   
7. (14291182625542246875*(x - 650))/(9007199254740992*(x - 1000)) + ...
   
8. (330429464948143465625*(x - (56830*x - 48065700)/(763*x - 706170)))/(18014398509481984*(x - 1000)) + ...
   
9. (330429464948143465625*(x + (56830*x - 48065700)/(763*x - 706170) - 1000))/(18014398509481984*(x - 1000)) -...
   
10. (5083*gama*(x - 1000))/20 + (5083*gama*x^2)/(10*(2*x - 2000)) + 1600000;
    
11. Mcr=(357279565638556171875*(x - 350))/(4503599627370496*(x - 1000)) - ...
    
12. (357279565638556171875*(x - 450))/(4503599627370496*(x - 1000)) - ...
    
13. (1071838696915668515625*(x - 550))/(4503599627370496*(x - 1000)) + ...
    
14. (1071838696915668515625*(x - 650))/(4503599627370496*(x - 1000)) + ...
    
15. (330429464948143465625*(x - (56830*x - 48065700)/(763*x - 706170))*((56830*x - 48065700)/...
    
16. (763*x - 706170) - 500))/(18014398509481984*(x - 1000)) - ...
    
17. (330429464948143465625*((56830*x - 48065700)/(763*x - 706170) - 500)*(x + ...
    
18. (56830*x - 48065700)/(763*x - 706170) - 1000))/(18014398509481984*(x - 1000)) - ...
    
19. (5083*gama*(x/3 + 500/3)*(x - 1000))/20 + (5083*gama*x^2*(x/3 - 500))/(10*(2*x - 2000));
    
20. y=solve(p1,Mcr)

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>> vpa(y.gama,3)

ans =

         -.2
.5-.56e-1*i
.5+.56e-1*i


>> vpa(y.x,3)

ans =

      .100e4
929.+6.55*i
929.-6.55*i