Solving 3 equations with 3 unknowns
显示 更早的评论
Dear members;
I would like to solve 3 equations using matlab. following are the 3 equations.
0.0972=ve*ln(mo/(mo-1010mp))
0.11285=ve*ln((mo-1010mp)/(mo-2145mp))
0.10953=ve*ln((mo-2145mp)/(mo-3395mp))
The unknowns in these equations are ve, mo and mp. is there a way to solve for the unknowns?
Thanks in advance
回答（3 个）
Azzi Abdelmalek
2013-3-5
syms me ve mo mp
eq1=0.0972-ve*log(mo/me)
eq2=0.11285-ve*log((mo-1010*mp)/(mo-2145*mp))
eq3=0.10953-ve*log((mo-2145*mp)/(mo-3395*mp))
solve(eq1,eq2,eq3,ve,mo,mp)
Youssef Khmou
2013-3-5
hi try ,
D=solve('x*log(y/a)=0.0972','x*log((y-1010*z)/(y-2145*z))=0.11285','x*log((y-2145*z)/(y-3395*z))=0.10953','x','y','z')
what is me? it is replaced with a
6 个评论
Hamza
2013-3-5
Youssef Khmou
2013-3-5
ok, then Symbolic Math toolbox is missing ...
Hamza
2013-3-5
Youssef Khmou
2013-3-6
The solution could not be found ! check again the equations .
Walter Roberson
2013-3-6
编辑：Walter Roberson
2013-3-6
One solution is
mo = me, mp = 0, ve = infinity
There might be other solutions; I have my system checking.
... There do not appear to be any other real solutions.
Hamza
2013-3-6
Roger Stafford
2013-3-6
I claim there are either no solutions or infinitely many solutions to your three equations, and I'll tell you why, Hamza. By manipulating the equations appropriately one can rewrite them in the form:
exp(0.0972/ve) = 1/(1-1010*r)
exp(0.11285/ve) = (1-1010*r)/(1-2145*r)
exp(0.10953/ve) = (1-2145*r)/(1-3395*r)
where r = mp/mo. As you can see from this, you have in effect three equations but only two unknowns, namely 've' and 'r', and they are unlikely to have a solution. You can find out if that is so by solving, say, just the first two of these equations. These two can be expressed as:
1-1010*r = exp(-0.0972/ve)
1-2145*r = (1-2145*r)/(1-1010*r) * (1-1010*r)
= exp(-0.11285/ve)*exp(-0.0972/ve)
= exp(-.21005/ve)
Solving for r in each equation gives
r = (1-exp(-0.0972/ve))/1010 = (1-exp(-.21005/ve))/2145
2145*(1-exp(-0.0972/ve)) = 1010*(1-exp(-.21005/ve))
1010*exp(-.21005/ve)-2145*exp(-0.0972/ve)+1135 = 0
You can use matlab's 'fzero' to solve this last equation for 've' and from that determine 'r'. As I say, any such solutions are unlikely to also satisfy the third equation above. If they do, then you will have infinitely many solutions corresponding to all the ways of satisfying r = mp/mo.
类别
在 帮助中心 和 File Exchange 中查找有关 Particle Swarm 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
