How do I solve this set of equations using MATLAB?
1 次查看(过去 30 天)
显示 更早的评论
I am trying to solve the following equations for the variable
:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1185413/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1185418/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1185423/image.png)
for that I wrote the following:
syms M n_1 n_2 n_3 th1 th2 th3
eqns = [M == ( (n_2*cos(th2) - n_3*cos(th3))/(n_2*cos(th2) + n_3*cos(th3)) )*...
( (n_2*cos(th2) + n_1*cos(th1))/(n_2*cos(th2) - n_1*cos(th1)) ) , ...
n_1*sin(th1) == n_2*sin(th2) , n_1*sin(th1) == n_3*sin(th3) ];
S = solve(eqns, [n_2])
But when I run the code I get that:
Empty sym: 0-by-1
What have I done wrong? How do I solve multiple equations?
0 个评论
回答(2 个)
Torsten
2022-11-8
You want to solve for one unknown - thus you only need one of the two equations.
If you want to solve for n1, n2 and n3, you have to specify this is the solve command.
But MATLAB cannot find an analytical solution, as you can see below.
syms M n_1 n_2 n_3 th1 th2 th3
eqns = [M == ( (n_2*cos(th2) - n_3*cos(th3))/(n_2*cos(th2) + n_3*cos(th3)) )*...
( (n_2*cos(th2) + n_1*cos(th1))/(n_2*cos(th2) - n_1*cos(th1)) ) , ...
n_1*sin(th1) == n_2*sin(th2) , n_1*sin(th1) == n_3*sin(th3) ];
S = solve(eqns, [n_1,n_2,n_3])
5 个评论
John D'Errico
2022-11-8
I would note there is pretty much never an analytical solution to a problem, where a variable appears both inside and outside of a trig function. Thus anything of the general form x*sin(x) = c, will generally have no algebraic/analytical solution, even if it has a numerical solution.
Torsten
2022-11-8
As you can see from the below analysis, there is only the solution n_1 = n_2 = n_3 = 0 without conditions on the angles th1, th2 and th3.
syms M n_1 n_2 n_3 th1 th2 th3
f = M *(n_2*cos(th2) + n_3*cos(th3))*(n_2*cos(th2) - n_1*cos(th1)) - (n_2*cos(th2) - n_3*cos(th3))*(n_2*cos(th2) + n_1*cos(th1));
f = subs(f,[n_2 n_3],[n_1*sin(th1)/sin(th2),n_1*sin(th1)/sin(th3)])
f = simplify(f)
0 个评论
另请参阅
类别
在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!