Question

matlab求解三元二次方程组

x1=-226.11;
y1=238.802;
z1=-1577;
x2=223.1317;
y2=201.5533;
z2=-1577;
x3=-277.2719;
y3=-202.0605;
z3=-1577;
与求解方程组：
(t1*x1-t2*x2)^2+(t1*y1-t2*y2)^2+(t1*z1-t2*z2)^2=532.8689^2
(t1*x1-t3*x3)^2+(t1*y1-t3*y3)^2+(t1*z1-t3*z3)^2=532.8689^2
(t3*x3-t2*x2)^2+(t3*y3-t2*y2)^2+(t3*z3-t2*z2)^2=753.5904^2
从中解出t1，t2，t3

只需要解出近似解就可以了，solve解不出来的。

Answer 1

x1=-226.11;
y1=238.802;
z1=-1577;
x2=223.1317;
y2=201.5533;
z2=-1577;
x3=-277.2719;
y3=-202.0605;
z3=-1577;
syms t1 t2 t3
eq1=(t1*x1-t2*x2)^2+(t1*y1-t2*y2)^2+(t1*z1-t2*z2)^2-532.8689^2;
eq2=(t1*x1-t3*x3)^2+(t1*y1-t3*y3)^2+(t1*z1-t3*z3)^2-532.8689^2;
eq3=(t3*x3-t2*x2)^2+(t3*y3-t2*y2)^2+(t3*z3-t2*z2)^2-753.5904^2;
[t1 t2 t3]=solve(eq1,eq2,eq3,'t1','t2','t3')
楼主我用solve可以解出解来，你参考一下

追问

能不能把结果发出来一下？可能我的机器不行。

追答

t1 =

-1.0509173508545735104340338689947
-1.1698934808360810991826320184508
1.0509173508545735104340338689947
1.1698934808360810991826320184508
0.010396634113083991776989880165808*i - 1.2019462220480859491977964180343
- 0.010396634113083991776989880165808*i - 1.2019462220480859491977964180343
1.2019462220480859491977964180343 - 0.010396634113083991776989880165808*i
0.010396634113083991776989880165808*i + 1.2019462220480859491977964180343

t2 =

-1.1697089782522916388945379925719
-1.1913186512726991219844892128139
1.1697089782522916388945379925719
1.1913186512726991219844892128139
0.057634634834530744446137087224216*i - 1.138347026247663883595166143394
- 0.057634634834530744446137087224216*i - 1.138347026247663883595166143394
1.138347026247663883595166143394 - 0.057634634834530744446137087224216*i
0.057634634834530744446137087224216*i + 1.138347026247663883595166143394

t3 =

-1.174266184126665874532701817206
-1.0359709975279320067152227120205
1.174266184126665874532701817206
1.0359709975279320067152227120205
- 0.0089114677978635435253876332051359*i - 1.2032654076846048324649767119272
0.0089114677978635435253876332051359*i - 1.2032654076846048324649767119272
0.0089114677978635435253876332051359*i + 1.2032654076846048324649767119272
1.2032654076846048324649767119272 - 0.0089114677978635435253876332051359*i