Empty sym: 0-by-1

I am trying to get the solve the equation-system, however i keep getting Empty sym: 0-by-1 as an answer

P1_DIC = [-12.82; -8.1331; 0.1719];

P2_DIC = [-0.6782; 12.0748; 0.8961];

P3_DIC = [-23.8363; 2.3239; -5.5797];

P4_DIC = [-13.3786; 14.0454; -0.4767];

P1_TG = [379; 354];

P2_TG = [438; 240];

P3_TG = [305; 294];

P4_TG = [372; 225];

v1_DIC = P4_DIC - P1_DIC;

v2_DIC = P2_DIC - P1_DIC;

v3_DIC = P3_DIC - P1_DIC;

syms alfa bta gama v1_3 v2_3 v3_3 a

v1_TG = [P4_TG(1)-P1_TG(1); P4_TG(2)-P1_TG(2); v1_3];

v2_TG = [P2_TG(1)-P1_TG(1); P2_TG(2)-P1_TG(2); v2_3];

v3_TG = [P3_TG(1)-P1_TG(1); P3_TG(2)-P1_TG(2); v3_3];

T11 = cos(alfa)*cos(bta);

T12 = cos(alfa)*sin(bta)*sin(gama)-sin(alfa)*cos(gama);

T13 = cos(alfa)*sin(bta)*cos(gama)+sin(alfa)*sin(gama);

T21 = sin(alfa)*cos(bta);

T22 = sin(alfa)*sin(bta)*sin(gama)+cos(alfa)*cos(bta);

T23 = sin(alfa)*sin(bta)*cos(gama)-cos(alfa)*sin(gama);

T31 = -sin(bta);

T32 = cos(bta)*sin(gama);

T33 = cos(bta)*cos(gama);

eqn{1} = v1_TG(1)*T11 + v1_TG(2)*T12 + v1_TG(3)*T13 == v1_DIC(1);

eqn{2} = v1_TG(1)*T21 + v1_TG(2)*T22 + v1_TG(3)*T23 == v1_DIC(2);

eqn{3} = v1_TG(1)*T31 + v1_TG(2)*T32 + v1_TG(3)*T33 == v1_DIC(3);

eqn{4} = v2_TG(1)*T11 + v2_TG(2)*T12 + v2_TG(3)*T13 == v2_DIC(1);

eqn{5} = v2_TG(1)*T21 + v2_TG(2)*T22 + v2_TG(3)*T23 == v2_DIC(2);

eqn{6} = v2_TG(1)*T31 + v2_TG(2)*T32 + v2_TG(3)*T33 == v2_DIC(3);

eqn{7} = a^2 * norm(v3_TG)^2 == norm(v3_DIC)^2 ;

s = solve(eqn{1},eqn{2},eqn{3},eqn{4},eqn{5},eqn{6}, alfa, bta, gama, v1_3, v2_3, v3_3, a)

do you guys have an idea why?

Answer 1

[Rasmita]

Hi,

It is my understanding that, you want to know why you are getting empty syms of 0-by-1 as output when solving above system of equations.

To find a numeric solution, you must give same number of equations as the number of variables in input to 'solve' function.

In this line of code:

s = solve(eqn{1},eqn{2},eqn{3},eqn{4},eqn{5},eqn{6}, alfa, bta, gama, v1_3, v2_3, v3_3, a)

write the inputs to the ‘solve’ function as an array of equations and an array of variables, like this:

s = solve([eqn{1},eqn{2},eqn{3},eqn{4},eqn{5},eqn{6}, eqn{7}], [alfa, bta, gama, v1_3, v2_3, v3_3, a])

After correcting above syntax also you might face the same issue because, the solver returns an empty solution of 0-by-1 syms when no solutions exist for that system of equations.

For more information on this, refer following documentation:

https://www.mathworks.com/help/symbolic/sym.solve.html

Hope this helps!

Regards,

Rasmita