eig(a,b) matlab symbolic

hi, need some help

How do you find the eigenvalues of 2 symbolic matrix in Matlab?

i have this:

syms k1 k2 kx m1 m2 W
K =  [ k1 + kx     -kx      0
    -kx      k2 + kx    -k2
    0        -k2         k2]
M =[ 2*m1      0       0
    0       2*m2     m2
    0        m2      2*m2]
[V,D]=eig(K,M);

it retun me

Error using sym/eig

Too many input arguments.

but when i give value to k1 k2 m1 m2 its work

i need D with symbolic value some one can help me please

Answer 1

[Sam Chak]

Hi @mohamdi mohamed

Are you looking for the analytical solution like this?

syms k1 k2 kx m1 m2

K =  [k1+kx -kx  0;
     -kx  k2+kx -k2;
       0    -k2  k2]

K = 

M =[2*m1    0    0;
       0 2*m2   m2;
       0   m2 2*m2]

M = 

[V, Lambda] = eig(M*inv(K))

V = 

Lambda = 

[mohamdi mohamed]

oh thank you sir

[Sam Chak]

@mohamdi mohamed, You are welcome!

[mohamdi mohamed]

hi @Sam Chak

can you please tell me how did you do this

i try to do it by my self

and its look very hard very long very complicate

how did you make this simplification

[Sam Chak]

Hi @mohamdi mohamed

Since you asked for a symbolical solution for eigenvalues, then that's the one produced by MATLAB eig() function that requires solving 3rd-degree polynomial equation. A 3rd-degree polynomial has analytical solutions. However, because there are many other parameters in the matrices, the given solution looks complicated.

I think the solution is already in the simplest form, as I don't find any terms that can be cancelled out or reducible. If you wish to solve it by hand, please look up Cardano's formula.

Answer 2

[mohamdi mohamed]

i find this way

Dyn= M*inv(K)

[V,lambda]=eig(Dyn)