Empty sym: 0-by-1

i used this code

F1 = [0 0 6];

F2 = [-1.7678 3.0619 3.5355];

F3 = [2 2 2.8284];

FR = F1 + F2 + F3;

r1 = [2 6 0];

r2 = [4 0 0];

M = cross(r1,F1)+cross(r2,F2);

uFR = FR/norm(FR);

syms x y

R1 = dot(M,uFR)*uFR + cross([x y 0],FR) == M

R2= norm([x y 0]/norm([x y 0])) == 1

sol = solve([R1,R2],[x,y]);

and when i wrote "sol.x" it returns "ans = Empty sym: 0-by-1"

could you check what i did wrong why it can't calculate x and y

Answer 1

[Mahesh Taparia]

Hi,

As per your code, R1 consists of 3 equations with two unknowns. Also, there is no need of R2 as it will always give the value 1 for all x and y as numerator and denominator cancels each other. As per the solve command, the argument should be the equations followed by the variables. So, in your case it should be:

sol = solve([R1(1),R1(3)],[x,y]); 

Or

sol = solve([R1(1),R1(2)],[x,y]);

and so on. Because R1 itself consists of 3 equations, it cannot be used directly.

Moreover, the solution will be more precise if ‘vpasolve’ will be used instead of solve command. This will show a very small variation in the value of x and y if it is executed with multiple equations due to more precision. Execute the following code and see the difference in result:

sol = vpasolve([R1(1),R1(3)],[x,y]); 
sol = vpasolve([R1(1),R1(2)],[x,y]);