How to solve the following non linear system of equations?

Considering that the only unknows are q11, q21, q12, q22, is there any matlab function to get the solution? Is there a possibility that there exists no solution? We have 4 equations and 4 unknonws, the other variables apart from q11, q21, q12, q22 are all known.

[Walter Roberson]

(Which is to say that you would probably get more response if you were to type the equations out, as not many people are going to bother to type them out for testing purposes.)

[Walter Roberson]

It looks plausible that you could use the symbolic toolbox. However, I can see that if there are any solutions there are multiple solutions due to the ^2 of the second two equations; and the cos() and sin() and cosh() and sinh() make it likely that there are an infinite number of solutions.

These look to me to possibly be rotation matrices such as for a robot arm. Such equations seldom have unique solutions.

[Alex O]

Thanks for your answer walter, this equations are result of the development of the eulerbernoulli beam theory and the vibration based theory considering unknown stiffnes. I will share them as soon as i have them written in matlab

Answer 1

[Bshara Murr]

Not sure how do you read your system and get 4 equations with 4 unknowns. However for such problems you must use the symbolic toolbox if you want the computer to generate your system. And try slove it will do the work. I have worked on a similar problem but i have forgotten all the details on how i did it. If you want i can send you the code. But as far as i remember "solve" solves nonlinear equations.

[Walter Roberson]

The notations indicate that q11, q12, q21, q22 are the unknowns; everything else is to be presumed known.

The first two equations are det() equal to 0; the last two equations have the difference of a couple of ^2 terms equal to 0. That gives four equations and four unknowns.

However... I cannot seem to find any msolve()

[Bshara Murr]

yes i am sorry the function is solve my bad, i'll fix it in my answer.