I would like to solve a 2x2 system of equations. Can anyone help me please?

Hello, i have 2 equations with two unknowns. How matlab can solve the system?

The equations are:

1) (t-0.1)sqrt(1-(121-(t-0.1)^2*400*cos(theta0))=(8.66*t-10)/(20cos(theta0))

2) cos(theta0)=sqrt(1-(8.66*t-4.9*t^2+4.9*(t-0.1)^2)/((t-0.1)^2*400))

The unknowns are theta0 and t.

I am looking forward for your information.

Thank you in advance for any help you can provide.

Answer 1

[Torsten]

Did you try MATLAB's "solve":

https://de.mathworks.com/help/symbolic/solve.html

?

Best wishes

Torsten.

[Amy Tsigouris]

Thank you for your reply.

I tried "solve" in this form:

syms theta0 u0

eqns=[ (t-0.1)sqrt(1-(121-(t-0.1)^2*400*cos(theta0))= =(8.66*t-10)/(20cos(theta0)) , cos(theta0)= = sqrt(1-(8.66*t-4.9*t^2*(t-0.1)^2*400)))];

vars=[theta0 u0];

[soltheta0,solu0]solve(eqns,vars);

From MathWorks:

syms u v eqns = [2*u^2 + v^2 == 0, u - v == 1];

vars = [v u];

[solv, solu] = solve(eqns, vars)

But it gives me error. What I am doing wrong?

Thank you for your time.

Answer 2

[Torsten]

syms theta t 

eqns=[ (t-0.1)*sqrt(1-(121-(t-0.1)^2*400*theta)==(8.66*t-10)/(20*theta) , theta == sqrt(1-(8.66*t-4.9*t^2*(t-0.1)^2*400)))];

vars=[theta t];

[soltheta,solt]=solve(eqns,vars);

Then theta0=acos(soltheta) and t=solt are solutions of your system.

Best wishes

Torsten.

[Amy Tsigouris]

Torsten again error...

 Error: Unbalanced or unexpected parenthesis or bracket.

in this line: vars [theta t];

[Torsten]

I don't see any such line in the code, only

vars=[theta t];

Best wishes

Torsten.

[Torsten]

Here is the solution MATHEMATICA gets:

http://www.wolframalpha.com/input/?i=Solve%5B%7B(t-0.1)*Sqrt%5B(1-(121-(t-0.1)%5E2*400*theta))%5D%3D%3D(8.66*t-10)%2F(20*theta),theta%3D%3DSqrt%5B1-(8.66*t-4.9*t%5E2*(t-0.1)%5E2*400)%5D%7D,%7Btheta,t%7D%5D

The problem is that all solutions listed are complex-valued.

Best wishes

Torsten.