Help with state representation of my 3-mass 2-spring system

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Starting from this information, I have managed to obtain this state representation. I wanted to ask for your confirmation to know if it is correct, or if it is not, where I made a mistake. Thank you for your attention.
this are my matrix :
A = [ 0 1 0 0 0 0;
-k0/m1 0 k0/m1 0 0 0;
0 0 0 1 0 0;
0 0 -k0/m2 0 k0/m2 0;
0 0 0 0 0 1;
0 0 0 0 -k0/m3 0];
B = [1/m1;
0;
0;
0;
0;
0];
C = [1 0 0 0 0 0];
D = 0;
  3 个评论
Cristian Rohozneanu
编辑:Cristian Rohozneanu 2024-1-17
I apologize; I forgot to mention that the cubic term should not be considered. Therefore, k(\delta_i) = k_0 * \delta_i
Cristian Rohozneanu
编辑:Cristian Rohozneanu 2024-1-17
Furthermore, the matrices I have derived are as follows. I apologize for any confusion.
A = [0 0 0 1 0 0;
0 0 0 0 1 0;
0 0 0 0 0 1;
-(k0/m1) (k0/m1) 0 0 0 0;
(k0/m2) -(2*k0/m2) (k0/m2) 0 0 0;
0 (k0/m3) -(k0/m3) 0 0 0];
B = [1/m1; 0; 0; 0; 0; 0];
C = [0 1 0 0 0 0];

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回答(1 个)

James Tursa
James Tursa 2024-1-17
The k terms in the equations above appear to be non-linear. Your A matrix doesn't account for the cubic parts.
  1 个评论
Cristian Rohozneanu
编辑:Cristian Rohozneanu 2024-1-17
I forgot to mention that the cubic term should not be considered. Therefore, k(\delta_i) = k_0 * \delta_i
Furthermore, the matrices I have derived are as follows. I apologize for any confusion.
A = [0 0 0 1 0 0;
0 0 0 0 1 0;
0 0 0 0 0 1;
-(k0/m1) (k0/m1) 0 0 0 0;
(k0/m2) -(2*k0/m2) (k0/m2) 0 0 0;
0 (k0/m3) -(k0/m3) 0 0 0];
B = [1/m1; 0; 0; 0; 0; 0];
C = [0 1 0 0 0 0];

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