Matlab ~ linear equation?

Question

do any one know how to solve this equation in MATLAB?

F_I*cosd(alpha_I) - F_C(cosd(alpha_C)) = 0  
F_I*sind(alpha_I) - F_T_1 + F_C*sind(alpha_C) = 0  
F_T_1*abs(x_F_C-x_T_1) - F_I*sind(alpha_I)*abs(x_F_C-x_F_I) - F_I*cosd(alpha_I)*abs(y_F_C-y_F_I) = 0

I KNOW:

alpha_I | F_T_1 | x_F_C | x_T_1 | x_F_I | y_F_C | y_F_I

I DON'T know (and want to know):

F_I | F_C | alpha_C

The problem is in F_C*cosd(alpha_C), which are two variables so I don't know what to write in Ax=B matrix in A.

This is not a linear equation since it contains the cosd of an unknown. Consider using nonlinear solver (optimization) routines, like lsqnonlin. Do you have the optimization toolbox? — Floris
It would be helpful to write your equation in terms of unknowns x(1:3) and knowns k(1:n) simplified as much as possible (so abs(x_F_C-x_F_I) becomes, say, k(5). It will then be much easier to write the target function to minimize with the solver. — Floris
In your first equation, do you mean F_C(cosd(alpha_C)) or F_C*cosd(alpha_C) — Floris
I'm not so sure about the optimization toolbox but I'm using the newest matlab. I just want to solve system of three equations witch 3 variables. That can't be so hard, would it? For the 'abs(x_F_C-x_F_I)' I can write '476' etc. It's a length from a point to another point. I'm trying to solve this: songokussj4.abonas.com/screeny/2013-03-24_183955.png It just came to my mind, what about if I name F_Csind(alpha_C) = AA and F_Ccosd(alpha_C) = BB and try to solve with variables F_I, AA, AB and then I will somewhat try to solve alpha_C and F_C in AA,AB ? — Jan Verner

Floris Floris · Accepted Answer · 2013-03-24T17:39:44

The third equation contains only one unknown, namely F_I. You can therefore explicitly solve for that, which leaves you with only two equations and two unknowns:

F_I= (F_T_1*abs(x_F_C-x_T_1)/(sind(alpha_I)*abs(x_F_C-x_F_I)+cosd(alpha_I)*abs(y_F_C-y_F_I))

Now your first two equations are basically of the form

a*sind(b)=c
a*cosd(b)=d

With a, b unknown. Divide them to get

tand(b) = c/d

This gives you b (alpha_C), and now solving for a (F_C) is trivial.

Matlab ~ linear equation?

1 Answers