切换到宽版

 找回密码
 注册
Simdroid-非首页
Simwe仿真论坛(forum.simwe.com)，CAE/CAD/CAM/，FEA/FEM/有限元分析论坛---(手机验证注册)»论坛 › ..:: 科学软件专区 › K01：MatLab › 如何才能快速的解出这组方程？
返回列表 发新帖
查看: 247|回复: 12

如何才能快速的解出这组方程？

[复制链接]
youbin
发表于 2011-5-13 09:05:16 | 显示全部楼层 |阅读模式 来自 湖北武汉
本帖最后由 youbin 于 2011-5-15 15:33 编辑

下面是解一组方程，但matlab解了好久也没有结果，只提示busy.请各位高手指点一下，如何才能快速的解出这组方程？

r1=380
r2=909.63
r3=690.61
r4=825.72
r5=3500
x11=0
y11=0
x12=380
y12=0
x13=380+909.63
y13=0
x14=380+909.63+380
y14=0
x21=0+3500
y21=0
x22=380+3500
y22=0
x23=380+909.63+3500
y23=0
x24=380+909.63+380+3500
y24=0


e1='(x11-x15)^2+(y11-y15)^2-r3^2=0'
e2='(x14-x16)^2+(y14-y16)^2-r3^2=0'
e3='(x15-x16)^2+(y15-y16)^2-r4^2=0'
e4='(x15-x25)^2+(y15-y25)^2-r5^2=0'
e5='(x15-x26)^2+(y15-y26)^2-r5^2=0'
e6='(x21-x25)^2+(y21-y25)^2-r3^2=0'
e7='(x24-x26)^2+(y24-y26)^2-r3^2=0'
e8='(x25-x26)^2+(y25-y26)^2-r4^2=0'

syms x15 y15 x16 y16 x25 y25 x26 y26;
[x15,y15,x16,y16,x25,y25,x26,y26]=solve(e1,e2,e3,e4,e5,e6,e7,e8,'x15','y15','x16','y16','x25','y25','x26','y26');
x15=vpa(x15,4);
y15=vpa(y15,4);
x16=vpa(x16,4);
y16=vpa(y16,4);
x25=vpa(x25,4);
y25=vpa(y25,4);
x26=vpa(x26,4);
y26=vpa(y26,4);


首先多谢各位高手指点，其实这是一个多连杆机构，在solidwork中放样证明，肯定是有实数解的。
上面方程是用各点的距离列的方程。
本想如果能很快解出来，再将点（x11,y11)绕（x12,y12)转动,下部其他点不变，来求(x15,y15)(x16,y16)(x25,y25)(x26,y26)这四个点的位置。
可能解题思路有问题，请各位高手指点，有没有更好的办法。先谢了！
matlab

本帖子中包含更多资源

您需要 登录 才可以下载或查看，没有账号？注册

×

相关帖子
回复

使用道具 举报

mhkmars
发表于 2011-5-13 13:39:37 | 显示全部楼层 来自 陕西西安
Simdroid开发平台
1# youbin
你这个定义了太多的符号变量，且不说你这个是否有精确解析解，符号运算与数值运算的速度就不是一个量级的，建议你改写成数值计算，速度快

评分

1

查看全部评分

回复 赞 不支持

使用道具 举报

lin2009
发表于 2011-5-13 22:33:32 | 显示全部楼层 来自 湖南湘潭
实际需要参与符号计算的未知变量只有8个，Lz把问题弄复杂了：定义了21个变量，且全部卷入到了符号计算中。
这8个未知变量是通过8方程构成的方程组来求解的，这个方程组为非线性方程组（可能是某参数回归模型）。若找不到现成成熟的非线性方程组的求解函数（像是有一个Nonlinear?的工具箱），是很难用简单的形式改写成数值计算（需要自己编写迭代算法，且可能存在多解）。
Matlab并不擅长符号计算，要想快速的解出这个方程组，可用符号计算软件（maple、mathematic）计算。
回复 赞 不支持

使用道具 举报

mhkmars
发表于 2011-5-14 00:13:54 | 显示全部楼层 来自 陕西西安
3# lin2009
个人觉得改写还是比较容易的

  2. function y=simwe(x)
  3. r1=380;
  4. r2=909.63;
  5. r3=690.61;
  6. r4=87.63;
  7. r5=825.72;
  8. x11=0;
  9. y11=0;
  10. x12=380;
  11. y12=0;
  12. x13=380+909.63;
  13. y13=0;
  14. x14=380+909.63+380;
  15. y14=0;
  16. x21=0+3500;
  17. y21=0;
  18. x22=380+3500;
  19. y22=0;
  20. x23=380+909.63+3500;
  21. y23=0;
  22. x24=380+909.63+380+3500;
  23. y24=0;
  24. x15=x(1);
  25. y15=x(2);
  26. x16=x(3);
  27. y16=x(4);
  28. x25=x(5);
  29. y25=x(6);
  30. x26=x(7);
  31. y26=x(8);
  32. y=[(x11-x15)^2+(y11-y15)^2-r3^2;
  33. (x14-x16)^2+(y14-y16)^2-r3^2;
  34. (x15-x16)^2+(y15-y16)^2-r4^2;
  35. (x15-x25)^2+(y15-y25)^2-r5^2;
  36. (x15-x26)^2+(y15-y26)^2-r5^2;
  37. (x21-x25)^2+(y21-y25)^2-r3^2;
  38. (x24-x26)^2+(y24-y26)^2-r3^2;
  39. (x25-x26)^2+(y25-y26)^2-r4^2;];
复制代码

至于解法的话，fsolve可以，
  1. clc;clear;
  2. x0 = [1000,0,100*rand,100*unifrnd(-100,100,1,5)];
  3. options=optimset('MaxFunEvals',2000000,'MaxIter',500000);
  4. [x,fval] = fsolve(@simwe,x0,options)
复制代码

但是貌似这个初值比较难去，总是局部收敛到以下的点
  1. x =

  3. 1.0e+003 *

  5. Columns 1 through 6

  7. 1.7344 -0.0000 2.2062 -0.0001 2.7602 -0.0000

  9. Columns 7 through 8

  11. 3.4534 -0.0000


  14. fval =

  16. 1.0e+006 *

  18. 2.5310
  19. -0.1890
  20. 0.2150
  21. 0.3705
  22. 2.2735
  23. 0.0704
  24. 2.4684
  25. 0.4730
复制代码


不知道兄台在取初值上有没有什么建议
Ps:论坛上关于非线性问题的初值选择方面的解决好像不太多
回复 赞 不支持

使用道具 举报

lin2009
发表于 2011-5-14 09:55:55 | 显示全部楼层 来自 湖南湘潭
初始值是比较难取，在这方面也没研究。
用maple求解可得到24组解：
{x15 = 2383.468881+39.68646842*I, x16 = 732.8414767-.6940225425*I, x25 = 4349.699439+30.29439120*I, x26 = 4337.530242-158.7618668*I
, y15 = 41.46465317-2281.255364*I, y16 = 1.027171091-632.9542943*I, y25 = 51.81348409-496.8036341*I, y26 = 260.1285567-507.8477837*I},
{x15 = 2383.468881+39.68646842*I, x16 = 3248.845565+38.42930991*I, x25 = 4349.699439+30.29439120*I, x26 = 4337.530242-158.7618668*I
, y15 = 41.46465317-2281.255364*I, y16 = 42.72830714-1420.326908*I, y25 = 51.81348409-496.8036341*I, y26 = 260.1285567-507.8477837*I},
{x15 = 2383.468881+39.68646842*I, x16 = 732.8414767-.6940225425*I, x25 = 4349.699439+30.29439120*I, x26 = 4337.530242-158.7618668*I
, y15 = -41.46465317+2281.255364*I, y16 = -1.027171091+632.9542943*I, y25 = -51.81348409+496.8036341*I, y26 = -260.1285567+507.8477837*I},
{x15 = 2383.468881+39.68646842*I, x16 = 3248.845565+38.42930991*I, x25 = 4349.699439+30.29439120*I, x26 = 4337.530242-158.7618668*I
, y15 = -41.46465317+2281.255364*I, y16 = -42.72830714+1420.326908*I, y25 = -51.81348409+496.8036341*I, y26 = -260.1285567+507.8477837*I},
{x15 = 1901.093337+54.55181049*I, x16 = 743.5022554-1.533398994*I, x25 = 4303.553663-198.5292532*I, x26 = 4318.561366+42.18743766*I
, y15 = 58.54762444-1771.345711*I, y16 = 2.301403576-617.0683692*I, y25 = 327.8227993+486.6315247*I, y26 = 71.70316682+500.7366696*I},
{x15 = 1901.093337+54.55181049*I, x16 = 2791.631152+49.88603979*I, x25 = 4303.553663-198.5292532*I, x26 = 4318.561366+42.18743766*I
, y15 = 58.54762444-1771.345711*I, y16 = 63.23614875-885.1297120*I, y25 = 327.8227993+486.6315247*I, y26 = 71.70316682+500.7366696*I},
{x15 = 1901.093337+54.55181049*I, x16 = 743.5022554-1.533398994*I, x25 = 4303.553663-198.5292532*I, x26 = 4318.561366+42.18743766*I
, y15 = -58.54762444+1771.345711*I, y16 = -2.301403576+617.0683692*I, y25 = -327.8227993-486.6315247*I, y26 = -71.70316682-500.7366696*I},
{x15 = 1901.093337+54.55181049*I, x16 = 2791.631152+49.88603979*I, x25 = 4303.553663-198.5292532*I, x26 = 4318.561366+42.18743766*I
, y15 = -58.54762444+1771.345711*I, y16 = -63.23614875+885.1297120*I, y25 = -327.8227993-486.6315247*I, y26 = -71.70316682-500.7366696*I},
{x15 = 2112.365990+8048.337148*I, x16 = 694.9896190-11.26317699*I, x25 = 1684.273082+6.957312434*I, x26 = 2543.345965+7.109924184*I
, y15 = 8076.022101-2105.124708*I, y16 = 15.95968999-687.8295957*I, y25 = -7.522684626-1679.264796*I, y26 = -7.369272658-2533.856629*I},
{x15 = 2112.365990+8048.337148*I, x16 = 2948.147579+8047.753296*I, x25 = 1684.273082+6.957312434*I, x26 = 2543.345965+7.109924184*I
, y15 = 8076.022101-2105.124708*I, y16 = 8076.609189-1273.949726*I, y25 = -7.522684626-1679.264796*I, y26 = -7.369272658-2533.856629*I},
{x15 = 2112.365990+8048.337148*I, x16 = 694.9896190-11.26317699*I, x25 = 1684.273082+6.957312434*I, x26 = 2543.345965+7.109924184*I
, y15 = -8076.022101+2105.124708*I, y16 = -15.95968999+687.8295957*I, y25 = 7.522684626+1679.264796*I, y26 = 7.369272658+2533.856629*I},
{x15 = 2112.365990+8048.337148*I, x16 = 2948.147579+8047.753296*I, x25 = 1684.273082+6.957312434*I, x26 = 2543.345965+7.109924184*I
, y15 = -8076.022101+2105.124708*I, y16 = -8076.609189+1273.949726*I, y25 = 7.522684626+1679.264796*I, y26 = 7.369272658+2533.856629*I},
{x15 = 2112.365990-8048.337148*I, x16 = 694.9896190+11.26317699*I, x25 = 1684.273082-6.957312434*I, x26 = 2543.345965-7.109924184*I
, y15 = 8076.022101+2105.124708*I, y16 = 15.95968999+687.8295957*I, y25 = -7.522684626+1679.264796*I, y26 = -7.369272658+2533.856629*I},
{x15 = 2112.365990-8048.337148*I, x16 = 2948.147579-8047.753296*I, x25 = 1684.273082-6.957312434*I, x26 = 2543.345965-7.109924184*I
, y15 = 8076.022101+2105.124708*I, y16 = 8076.609189+1273.949726*I, y25 = -7.522684626+1679.264796*I, y26 = -7.369272658+2533.856629*I},
{x15 = 2112.365990-8048.337148*I, x16 = 694.9896190+11.26317699*I, x25 = 1684.273082-6.957312434*I, x26 = 2543.345965-7.109924184*I
, y15 = -8076.022101-2105.124708*I, y16 = -15.95968999-687.8295957*I, y25 = 7.522684626-1679.264796*I, y26 = 7.369272658-2533.856629*I},
{x15 = 2112.365990-8048.337148*I, x16 = 2948.147579-8047.753296*I, x25 = 1684.273082-6.957312434*I, x26 = 2543.345965-7.109924184*I
, y15 = -8076.022101-2105.124708*I, y16 = -8076.609189-1273.949726*I, y25 = 7.522684626-1679.264796*I, y26 = 7.369272658-2533.856629*I},
{x15 = 1901.093337-54.55181049*I, x16 = 743.5022554+1.533398994*I, x25 = 4303.553663+198.5292532*I, x26 = 4318.561366-42.18743766*I
, y15 = 58.54762444+1771.345711*I, y16 = 2.301403576+617.0683692*I, y25 = 327.8227993-486.6315247*I, y26 = 71.70316682-500.7366696*I},
{x15 = 1901.093337-54.55181049*I, x16 = 2791.631152-49.88603979*I, x25 = 4303.553663+198.5292532*I, x26 = 4318.561366-42.18743766*I
, y15 = 58.54762444+1771.345711*I, y16 = 63.23614875+885.1297120*I, y25 = 327.8227993-486.6315247*I, y26 = 71.70316682-500.7366696*I},
{x15 = 1901.093337-54.55181049*I, x16 = 743.5022554+1.533398994*I, x25 = 4303.553663+198.5292532*I, x26 = 4318.561366-42.18743766*I
, y15 = -58.54762444-1771.345711*I, y16 = -2.301403576-617.0683692*I, y25 = -327.8227993+486.6315247*I, y26 = -71.70316682+500.7366696*I},
{x15 = 1901.093337-54.55181049*I, x16 = 2791.631152-49.88603979*I, x25 = 4303.553663+198.5292532*I, x26 = 4318.561366-42.18743766*I
, y15 = -58.54762444-1771.345711*I, y16 = -63.23614875-885.1297120*I, y25 = -327.8227993+486.6315247*I, y26 = -71.70316682+500.7366696*I},
{x15 = 2383.468881-39.68646842*I, x16 = 732.8414767+.6940225425*I, x25 = 4349.699439-30.29439120*I, x26 = 4337.530242+158.7618668*I
, y15 = 41.46465317+2281.255364*I, y16 = 1.027171091+632.9542943*I, y25 = 51.81348409+496.8036341*I, y26 = 260.1285567+507.8477837*I},
{x15 = 2383.468881-39.68646842*I, x16 = 3248.845565-38.42930991*I, x25 = 4349.699439-30.29439120*I, x26 = 4337.530242+158.7618668*I
, y15 = 41.46465317+2281.255364*I, y16 = 42.72830714+1420.326908*I, y25 = 51.81348409+496.8036341*I, y26 = 260.1285567+507.8477837*I},
{x15 = 2383.468881-39.68646842*I, x16 = 732.8414767+.6940225425*I, x25 = 4349.699439-30.29439120*I, x26 = 4337.530242+158.7618668*I
, y15 = -41.46465317-2281.255364*I, y16 = -1.027171091-632.9542943*I, y25 = -51.81348409-496.8036341*I, y26 = -260.1285567-507.8477837*I},
{x15 = 2383.468881-39.68646842*I, x16 = 3248.845565-38.42930991*I, x25 = 4349.699439-30.29439120*I, x26 = 4337.530242+158.7618668*I
, y15 = -41.46465317-2281.255364*I, y16 = -42.72830714-1420.326908*I, y25 = -51.81348409-496.8036341*I, y26 = -260.1285567-507.8477837*I})
回复 赞 不支持

使用道具 举报

TBE_Legend
发表于 2011-5-14 13:21:50 | 显示全部楼层 来自 黑龙江哈尔滨

mmtc解，无实数解

本帖最后由 TBE_Legend 于 2011-5-14 13:23 编辑
  1. In[1]:= Clear["Global`*"]
  2. r1 = 380;
  3. r2 = 90963/100;
  4. r3 = 69061/100;
  5. r4 = 8763/100;
  6. r5 = 82572/100;
  7. x11 = 0;
  8. y11 = 0;
  9. x12 = 380;
  10. y12 = 0;
  11. x13 = 380 + 90963/100;
  12. y13 = 0;
  13. x14 = 380 + 90963/100 + 380;
  14. y14 = 0;
  15. x21 = 0 + 3500;
  16. y21 = 0;
  17. x22 = 380 + 3500;
  18. y22 = 0;
  19. x23 = 380 + 90963/100 + 3500;
  20. y23 = 0;
  21. x24 = 380 + 90963/100 + 380 + 3500;
  22. y24 = 0;
  23. eqs = {(x11 - x15)^2 + (y11 - y15)^2 - r3^2 == 0,
  24.    (x14 - x16)^2 + (y14 - y16)^2 - r3^2 == 0,
  25.    (x15 - x16)^2 + (y15 - y16)^2 - r4^2 == 0,
  26.    (x15 - x25)^2 + (y15 - y25)^2 - r5^2 == 0,
  27.    (x15 - x26)^2 + (y15 - y26)^2 - r5^2 == 0,
  28.    (x21 - x25)^2 + (y21 - y25)^2 - r3^2 == 0,
  29.    (x24 - x26)^2 + (y24 - y26)^2 - r3^2 == 0,
  30.    (x25 - x26)^2 + (y25 - y26)^2 - r4^2 == 0};
  31. vars = Cases[eqs, _Symbol, Infinity];
  32. sol = NSolve[eqs, vars]
  33. sol // Length
  34. Out[25]= {{x15 -> 2112.37 - 8048.34 I, y15 -> -8076.02 - 2105.12 I,
  35.   x16 -> 2948.15 - 8047.75 I, y16 -> -8076.61 - 1273.95 I,
  36.   x25 -> 1684.27 - 6.95731 I, y25 -> 7.52268 - 1679.26 I,
  37.   x26 -> 2543.35 - 7.10992 I,
  38.   y26 -> 7.36927 - 2533.86 I}, {x15 -> 2112.37 + 8048.34 I,
  39.   y15 -> -8076.02 + 2105.12 I, x16 -> 2948.15 + 8047.75 I,
  40.   y16 -> -8076.61 + 1273.95 I, x25 -> 1684.27 + 6.95731 I,
  41.   y25 -> 7.52268 + 1679.26 I, x26 -> 2543.35 + 7.10992 I,
  42.   y26 -> 7.36927 + 2533.86 I}, {x15 -> 2112.37 - 8048.34 I,
  43.   y15 -> 8076.02 + 2105.12 I, x16 -> 2948.15 - 8047.75 I,
  44.   y16 -> 8076.61 + 1273.95 I, x25 -> 1684.27 - 6.95731 I,
  45.   y25 -> -7.52268 + 1679.26 I, x26 -> 2543.35 - 7.10992 I,
  46.   y26 -> -7.36927 + 2533.86 I}, {x15 -> 2112.37 + 8048.34 I,
  47.   y15 -> 8076.02 - 2105.12 I, x16 -> 2948.15 + 8047.75 I,
  48.   y16 -> 8076.61 - 1273.95 I, x25 -> 1684.27 + 6.95731 I,
  49.   y25 -> -7.52268 - 1679.26 I, x26 -> 2543.35 + 7.10992 I,
  50.   y26 -> -7.36927 - 2533.86 I}, {x15 -> 2112.37 - 8048.34 I,
  51.   y15 -> 8076.02 + 2105.12 I, x16 -> 694.99 + 11.2632 I,
  52.   y16 -> 15.9597 + 687.83 I, x25 -> 1684.27 - 6.95731 I,
  53.   y25 -> -7.52268 + 1679.26 I, x26 -> 2543.35 - 7.10992 I,
  54.   y26 -> -7.36927 + 2533.86 I}, {x15 -> 2112.37 + 8048.34 I,
  55.   y15 -> 8076.02 - 2105.12 I, x16 -> 694.99 - 11.2632 I,
  56.   y16 -> 15.9597 - 687.83 I, x25 -> 1684.27 + 6.95731 I,
  57.   y25 -> -7.52268 - 1679.26 I, x26 -> 2543.35 + 7.10992 I,
  58.   y26 -> -7.36927 - 2533.86 I}, {x15 -> 2112.37 - 8048.34 I,
  59.   y15 -> -8076.02 - 2105.12 I, x16 -> 694.99 + 11.2632 I,
  60.   y16 -> -15.9597 - 687.83 I, x25 -> 1684.27 - 6.95731 I,
  61.   y25 -> 7.52268 - 1679.26 I, x26 -> 2543.35 - 7.10992 I,
  62.   y26 -> 7.36927 - 2533.86 I}, {x15 -> 2112.37 + 8048.34 I,
  63.   y15 -> -8076.02 + 2105.12 I, x16 -> 694.99 - 11.2632 I,
  64.   y16 -> -15.9597 + 687.83 I, x25 -> 1684.27 + 6.95731 I,
  65.   y25 -> 7.52268 + 1679.26 I, x26 -> 2543.35 + 7.10992 I,
  66.   y26 -> 7.36927 + 2533.86 I}, {x15 -> 2383.47 - 39.6865 I,
  67.   y15 -> -41.4647 - 2281.26 I, x16 -> 3248.85 - 38.4293 I,
  68.   y16 -> -42.7283 - 1420.33 I, x25 -> 4349.7 - 30.2944 I,
  69.   y25 -> -51.8135 - 496.804 I, x26 -> 4337.53 + 158.762 I,
  70.   y26 -> -260.129 - 507.848 I}, {x15 -> 2383.47 + 39.6865 I,
  71.   y15 -> -41.4647 + 2281.26 I, x16 -> 3248.85 + 38.4293 I,
  72.   y16 -> -42.7283 + 1420.33 I, x25 -> 4349.7 + 30.2944 I,
  73.   y25 -> -51.8135 + 496.804 I, x26 -> 4337.53 - 158.762 I,
  74.   y26 -> -260.129 + 507.848 I}, {x15 -> 2383.47 + 39.6865 I,
  75.   y15 -> 41.4647 - 2281.26 I, x16 -> 3248.85 + 38.4293 I,
  76.   y16 -> 42.7283 - 1420.33 I, x25 -> 4349.7 + 30.2944 I,
  77.   y25 -> 51.8135 - 496.804 I, x26 -> 4337.53 - 158.762 I,
  78.   y26 -> 260.129 - 507.848 I}, {x15 -> 2383.47 - 39.6865 I,
  79.   y15 -> 41.4647 + 2281.26 I, x16 -> 3248.85 - 38.4293 I,
  80.   y16 -> 42.7283 + 1420.33 I, x25 -> 4349.7 - 30.2944 I,
  81.   y25 -> 51.8135 + 496.804 I, x26 -> 4337.53 + 158.762 I,
  82.   y26 -> 260.129 + 507.848 I}, {x15 -> 1901.09 + 54.5518 I,
  83.   y15 -> 58.5476 - 1771.35 I, x16 -> 2791.63 + 49.886 I,
  84.   y16 -> 63.2361 - 885.13 I, x25 -> 4303.55 - 198.529 I,
  85.   y25 -> 327.823 + 486.632 I, x26 -> 4318.56 + 42.1874 I,
  86.   y26 -> 71.7032 + 500.737 I}, {x15 -> 1901.09 - 54.5518 I,
  87.   y15 -> 58.5476 + 1771.35 I, x16 -> 2791.63 - 49.886 I,
  88.   y16 -> 63.2361 + 885.13 I, x25 -> 4303.55 + 198.529 I,
  89.   y25 -> 327.823 - 486.632 I, x26 -> 4318.56 - 42.1874 I,
  90.   y26 -> 71.7032 - 500.737 I}, {x15 -> 1901.09 - 54.5518 I,
  91.   y15 -> -58.5476 - 1771.35 I, x16 -> 2791.63 - 49.886 I,
  92.   y16 -> -63.2361 - 885.13 I, x25 -> 4303.55 + 198.529 I,
  93.   y25 -> -327.823 + 486.632 I, x26 -> 4318.56 - 42.1874 I,
  94.   y26 -> -71.7032 + 500.737 I}, {x15 -> 1901.09 + 54.5518 I,
  95.   y15 -> -58.5476 + 1771.35 I, x16 -> 2791.63 + 49.886 I,
  96.   y16 -> -63.2361 + 885.13 I, x25 -> 4303.55 - 198.529 I,
  97.   y25 -> -327.823 - 486.632 I, x26 -> 4318.56 + 42.1874 I,
  98.   y26 -> -71.7032 - 500.737 I}, {x15 -> 2383.47 - 39.6865 I,
  99.   y15 -> -41.4647 - 2281.26 I, x16 -> 732.841 + 0.694023 I,
  100.   y16 -> -1.02717 - 632.954 I, x25 -> 4349.7 - 30.2944 I,
  101.   y25 -> -51.8135 - 496.804 I, x26 -> 4337.53 + 158.762 I,
  102.   y26 -> -260.129 - 507.848 I}, {x15 -> 2383.47 + 39.6865 I,
  103.   y15 -> -41.4647 + 2281.26 I, x16 -> 732.841 - 0.694023 I,
  104.   y16 -> -1.02717 + 632.954 I, x25 -> 4349.7 + 30.2944 I,
  105.   y25 -> -51.8135 + 496.804 I, x26 -> 4337.53 - 158.762 I,
  106.   y26 -> -260.129 + 507.848 I}, {x15 -> 2383.47 + 39.6865 I,
  107.   y15 -> 41.4647 - 2281.26 I, x16 -> 732.841 - 0.694023 I,
  108.   y16 -> 1.02717 - 632.954 I, x25 -> 4349.7 + 30.2944 I,
  109.   y25 -> 51.8135 - 496.804 I, x26 -> 4337.53 - 158.762 I,
  110.   y26 -> 260.129 - 507.848 I}, {x15 -> 2383.47 - 39.6865 I,
  111.   y15 -> 41.4647 + 2281.26 I, x16 -> 732.841 + 0.694023 I,
  112.   y16 -> 1.02717 + 632.954 I, x25 -> 4349.7 - 30.2944 I,
  113.   y25 -> 51.8135 + 496.804 I, x26 -> 4337.53 + 158.762 I,
  114.   y26 -> 260.129 + 507.848 I}, {x15 -> 1901.09 + 54.5518 I,
  115.   y15 -> 58.5476 - 1771.35 I, x16 -> 743.502 - 1.5334 I,
  116.   y16 -> 2.3014 - 617.068 I, x25 -> 4303.55 - 198.529 I,
  117.   y25 -> 327.823 + 486.632 I, x26 -> 4318.56 + 42.1874 I,
  118.   y26 -> 71.7032 + 500.737 I}, {x15 -> 1901.09 - 54.5518 I,
  119.   y15 -> 58.5476 + 1771.35 I, x16 -> 743.502 + 1.5334 I,
  120.   y16 -> 2.3014 + 617.068 I, x25 -> 4303.55 + 198.529 I,
  121.   y25 -> 327.823 - 486.632 I, x26 -> 4318.56 - 42.1874 I,
  122.   y26 -> 71.7032 - 500.737 I}, {x15 -> 1901.09 - 54.5518 I,
  123.   y15 -> -58.5476 - 1771.35 I, x16 -> 743.502 + 1.5334 I,
  124.   y16 -> -2.3014 - 617.068 I, x25 -> 4303.55 + 198.529 I,
  125.   y25 -> -327.823 + 486.632 I, x26 -> 4318.56 - 42.1874 I,
  126.   y26 -> -71.7032 + 500.737 I}, {x15 -> 1901.09 + 54.5518 I,
  127.   y15 -> -58.5476 + 1771.35 I, x16 -> 743.502 - 1.5334 I,
  128.   y16 -> -2.3014 + 617.068 I, x25 -> 4303.55 - 198.529 I,
  129.   y25 -> -327.823 - 486.632 I, x26 -> 4318.56 + 42.1874 I,
  130.   y26 -> -71.7032 - 500.737 I}}
  131. Out[26]= 24
复制代码
回复 赞 不支持

使用道具 举报

lin2009
发表于 2011-5-14 20:37:08 | 显示全部楼层 来自 湖南湘潭
1# youbin
无实数解，另图形的标注有误！
r4 = 825.72 ?
r5 = 3500    ?
回复 赞 不支持

使用道具 举报

youbin
 楼主| 发表于 2011-5-15 16:16:52 | 显示全部楼层 来自 湖北
1# youbin
无实数解，另图形的标注有误！
r4 = 825.72 ?
r5 = 3500    ?
lin2009 发表于 2011-5-14 20:37


不好意思，copy时搞错了！已经改了！
回复 赞 不支持

使用道具 举报

lin2009
发表于 2011-5-15 21:01:02 | 显示全部楼层 来自 湖南湘潭
数据错误你已经更改过来的。
但是方程式错误你仍未更改！
...
e1='(x11-x15)^2+(y11-y15)^2-r3^2=0'
e2='(x14-x16)^2+(y14-y16)^2-r3^2=0'
e3='(x15-x16)^2+(y15-y16)^2-r4^2=0'
e4='(x15-x25)^2+(y15-y25)^2-r5^2=0'
e5='(x15-x26)^2+(y15-y26)^2-r5^2=0'
e6='(x21-x25)^2+(y21-y25)^2-r3^2=0'
e7='(x24-x26)^2+(y24-y26)^2-r3^2=0'
e8='(x25-x26)^2+(y25-y26)^2-r4^2=0'

...
中的
e5='(x15-x26)^2+(y15-y26)^2-r5^2=0'
应改为：
e5='(x16-x26)^2+(y16-y26)^2-r5^2=0'

更正后用Maple就可以得出24组实数解：
{x15=561.0396134,x16=1035.351055,x25=4061.039613,x26=4535.351055,y15=402.7117137, y16=-273.1892962,y25=402.7117137, y26=-273.1892962},
{x15=561.0396134,x16=1358.578098,x25=4061.039613,x26=4858.578098,y15=402.7117137, y16=616.5945883, y25=402.7117137, y26=616.5945883},
{x15=561.0396134,x16=1035.351055,x25=4061.039613,x26=4535.351055,y15=-402.7117137,y16=273.1892962, y25=-402.7117137,y26=273.1892962},
{x15=561.0396134,x16=1358.578098,x25=4061.039613,x26=4858.578098,y15=-402.7117137,y16=-616.5945883,y25=-402.7117137,y26=-616.5945883},

{x15=690.61,x16=1284.750828,x25=4190.61,x26=4784.750828,y15=0.,y16=573.4197372, y25=0.,y26=573.4197372},
{x15=690.61,x16=1284.750828,x25=4190.61,x26=4784.750828,y15=0.,y16=-573.4197372,y25=0.,y26=-573.4197372},

{x15=384.8791721,x16=979.02,     x25=3884.879172,x26=4479.02,    y15=573.4197372, y16=0.,          y25=573.4197372, y26=0.},
{x15=384.8791721,x16=979.02,     x25=3884.879172,x26=4479.02,    y15=-573.4197372,y16=0.,          y25=-573.4197372,y26=0.},
{x15=384.8791721,x16=1208.463463,x25=3884.879172,x26=4708.463463,y15=573.4197372, y16=514.0696426, y25=573.4197372, y26=514.0696426},
{x15=384.8791721,x16=1208.463463,x25=3884.879172,x26=4708.463463,y15=-573.4197372,y16=-514.0696426,y25=-573.4197372,y26=-514.0696426},

{x15=631.305931,x16=1104.378248,x25=4065.251752,x26=4538.324069,y15=279.9910597, y16=-396.7778085,y25=-396.7778085,y26=279.9910597},
{x15=631.305931,x16=1104.378248,x25=4065.251752,x26=4538.324069,y15=-279.9910597,y16=396.7778085, y25=396.7778085, y26=-279.9910597},

{x15=671.3974547,x16=1360.064415,x25=4171.397455,x26=4680.945513,y15=161.7641183, y16=617.3421424, y25=161.7641183, y26=-487.9852909},
{x15=671.3974547,x16=1360.064415,x25=4171.397455,x26=4680.945513,y15=-161.7641183,y16=-617.3421424,y25=-161.7641183,y26=487.9852909},

{x15=510.1758419,x16=1325.103711,x25=3844.526289,x26=4659.454158,y15=465.4704958, y16=598.5347175, y25=-598.5347175,y26=-465.4704958},
{x15=510.1758419,x16=1325.103711,x25=3844.526289,x26=4659.454158,y15=-465.4704958,y16=-598.5347175,y25=598.5347175, y26=465.4704958},

{x15=488.6844872,x16=998.2325453,x25=3809.565585,x26=4498.232545,y15=487.9852909,y16=-161.7641183,y25=-617.3421424,y26=-161.7641183},
{x15=488.6844872,x16=998.2325453,x25=3988.684487,x26=4498.232545,y15=487.9852909,y16=-161.7641183,y25=487.9852909, y26=-161.7641183},
{x15=488.6844872,x16=998.2325453,x25=3809.565585,x26=4498.232545,y15=-487.9852909,y16=161.7641183,y25=617.3421424, y26=161.7641183},
{x15=488.6844872,x16=998.2325453,x25=3988.684487,x26=4498.232545,y15=-487.9852909,y16=161.7641183,y25=-487.9852909,y26=161.7641183}
回复 赞 不支持

使用道具 举报

youbin
 楼主| 发表于 2011-5-16 14:19:51 | 显示全部楼层 来自 湖北武汉
本帖最后由 youbin 于 2011-5-16 14:34 编辑
数据错误你已经更改过来的。
但是方程式错误你仍未更改！
...

...
中的
e5='(x15-x26)^2+(y15-y26)^2-r5^2=0'
应改为：
e5='(x16-x26)^2+(y16-y26)^2-r5^2=0'

更正后用Maple就可以得出24组实数解：
{x ...
lin2009 发表于 2011-5-15 21:01

多谢lin2009兄的指点，我下个Maple试试.
Maple解方程的格式与matlab一样吗？lin2009兄可否将能在Maple中运行的程式贴上来，先谢了！
回复 赞 不支持

使用道具 举报

lin2009
发表于 2011-5-16 22:13:58 | 显示全部楼层 来自 湖南湘潭
本帖最后由 lin2009 于 2011-5-16 22:15 编辑

不太一样。程式如下：
  1. r1 := 380;
  2. r2 := 909.63;
  3. r3 := 690.61;
  4. r4 := 825.72;
  5. r5 := 3500;
  6. x11 := 0;
  7. y11 := 0;
  8. x12 := r1;
  9. y12 := 0;
  10. x13 := r1 + r2;
  11. y13 := 0;
  12. x14 := 2*r1 + r2;
  13. y14 := 0;
  14. x21 := x11 + r5;
  15. y21 := 0;
  16. x22 := x11 + r1;
  17. y22 := 0;
  18. x23 := x21 + r1 + r2;
  19. y23 := 0;
  20. x24 := x21 + 2*r1 + r2;
  21. y24 := 0;
  22. e1 := (x11-x15)^2 + (y11-y15)^2 - r3^2;
  23. e2 := (x14-x16)^2 + (y14-y16)^2 - r3^2;
  24. e3 := (x15-x16)^2 + (y15-y16)^2 - r4^2;
  25. e4 := (x15-x25)^2 + (y15-y25)^2 - r5^2;
  26. e5 := (x16-x26)^2 + (y16-y26)^2 - r5^2;
  27. e6 := (x21-x25)^2 + (y21-y25)^2 - r3^2;
  28. e7 := (x24-x26)^2 + (y24-y26)^2 - r3^2;
  29. e8 := (x25-x26)^2 + (y25-y26)^2 - r4^2;

  31. with(RealDomain)
  32. S := solve({e1, e2, e3, e4, e5, e6, e7, e8})
复制代码

评分

1

查看全部评分

回复 赞 不支持

使用道具 举报

youbin
 楼主| 发表于 2011-5-17 09:46:06 | 显示全部楼层 来自 湖北武汉
不太一样。程式如下：
r1 := 380;
r2 := 909.63;
r3 := 690.61;
r4 := 825.72;
r5 := 3500;
x11 := 0;
y11 := 0;
x12 := r1;
y12 := 0;
x13 := r1 + r2;
y13 := 0;
x14 := 2*r1 + r2;
y14 := 0;
x21 : ...
lin2009 发表于 2011-5-16 22:13

再次谢谢lin2009的热情帮助！也谢谢其他各位高手的指点！
回复 赞 不支持

使用道具 举报

huangwei_vicky
发表于 2011-6-26 18:34:53 | 显示全部楼层 来自 英国
一个非线性方程组，计算92步后出现提示
x =

  1.0e+005 *

   -0.0015
    1.7145
   -0.0000
    0.0000
    0.0004
    0.0093
    0.0000
    0.0000
    0.0007
    0.0004
   -0.0001

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunEvals = 1100 (the default value).

是不是就是初值选取问题，只得到局部收敛的结果？
回复 赞 不支持

使用道具 举报

返回列表 发新帖
高级模式
B Color Image Link Quote Code Smilies
您需要登录后才可以回帖 登录 | 注册

本版积分规则

Simapps系列直播

Archiver|小黑屋|联系我们|仿真互动网 ( 京ICP备15048925号-7 )

GMT+8, 2024-10-6 10:30 , Processed in 0.044647 second(s), 14 queries , Gzip On, MemCache On.

Powered by Discuz! X3.5 Licensed

© 2001-2024 Discuz! Team.

快速回复 返回顶部 返回列表