eig(a,b) matlab symbolic

Question

mohamdi mohamed 2023-3-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1930510-eig-a-b-matlab-symbolic

评论： Sam Chak 2023-4-18

采纳的回答： Sam Chak

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

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Answer 1

Sam Chak 2023-3-17

1
链接

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https://ww2.mathworks.cn/matlabcentral/answers/1930510-eig-a-b-matlab-symbolic#answer_1195160

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 =

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mohamdi mohamed 2023-4-17

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 2023-4-18

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.

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