Solution of system of linear equation

Dear All I need to solve the system of linear equations. I have 5 variables [t0 rp V theta alpha]. I need to calculate V, theta, alpha from the following three equations at different known values of t0 and rp using solve command but the following message appears. Note : the first guess for t0=20e-3;rp=0.2e-2. "Error using solve (line 278) Input with 3 variables and output with 2 variables are inconsistent."

a = 0.45611;b1= 17.03;
q1 = 0.062988; q2 = 18.68;
c1 = 0.0026617;c2= -0.9238;
g=9.81; S=0.012;ro=1000;mw=5;rw=0.2e-3;m_bar=0.8;

syms  V alpha theta
d1 =((1/2)*ro*V^2)*S*(a + b1*alpha^2);
Q = ((1/2)*ro*V^2)*S*(q1+q2*alpha);
T = ((1/2)*ro*V^2)*S*(c1 + c2*alpha);
eqn1 = -t0*g*sin(theta)+Q*alpha-d1 == 0;
eqn2 = t0*g*cos(theta)-Q-d1*alpha == 0;
eqn3 = T-m_bar*g*rp*cos(theta)==0;
eqns=[eqn1 eqn1 eqn3]
vars = [V alpha theta];
[solv, solu] = solve(eqns, vars)

[John D'Errico]

Please learn to format your code next time to be readable.

https://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup#answer_18099

Answer 1

[John D'Errico]

First, why do you think this is a system of LINEAR equations?

theta is one of your unknowns. The presence of sin(theta) and cos(theta) would be enough to make that false. Then we have alpha and V. They appear in various forms, thus alpha, alpha^2, and V^2, and as a product of the two.

This is a system of NONLINEAR equations. The mere presence of an addition sign does not make them linear.

The error return is simple to understand. You have THREE unknowns, thus V, alpha, theta. You have TWO outputs: solv and solu. You provide no place to return THREE results. When called with one output, solve is smart enough to stuff the results as fields of a struct. But when you ask for three outputs and provide two containers it gets confused, and rightfully so.

[Barkat]

Dear John D'Errico, You are right. Sorry the system is nonlinear

[John D'Errico]

More importantly, do you understand why an error arose?

[Barkat]

Yes Sir, But instead of using % code endvars = [V alpha theta]; [solv, solu] = solve(eqns, vars) How can I correct the response?