# Not your typical vertcat error. Weird behaviour with it.

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Mario Malic 2023 年 5 月 11 日

Hey,
I am not sure what's going on with editor, but I am having issues in understanding why does dxdt does not work properly. The error is about vertcat.
% Error using vertcat
% Dimensions of arrays being concatenated are not consistent.
Here is the code
m1 = parameters(1);
m2 = parameters(2);
k1 = parameters(3);
k2 = parameters(4);
d1 = parameters(5);
d2 = parameters(6);
% Output equation.
y = [x(1)]; % Displacement of the smaller mass
Now we execute each row of dxdt (further below) and we see the result
x(2)
ans = 50
(-((k1+k2)*x(1))/m1) + ((k2*x(3))/m1) - (((d1+d2)*x(2))/m1) + ((d2*x(4))/m1) +u(1)
ans = -416.6667
x(4)
ans = 50
(d2*x(2)/m2) - (d2*x(4)/m2) + (k2*x(1)/m2) - (k2*x(3)/m2) + 0
ans = 0
But if I want to do it this way, it doesn't work. Issue is that I have to add extra parentheses on the second element, but there should be none!
% State equations.
dxdt = [x(2); ...
(-((k1+k2)*x(1))/m1) + ((k2*x(3))/m1) - (((d1+d2)*x(2))/m1) + ((d2*x(4))/m1) +u(1); ...
x(4); ...
(d2*x(2)/m2) - (d2*x(4)/m2) + (k2*x(1)/m2) - (k2*x(3)/m2) + 0];
Error using vertcat
Dimensions of arrays being concatenated are not consistent.

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### 採用された回答

VBBV 2023 年 5 月 11 日
m1 = parameters(1)
m1 = 12
m2 = parameters(2)
m2 = 13
k1 = parameters(3)
k1 = 100
k2 = parameters(4)
k2 = 100
d1 = parameters(5)
d1 = 0
d2 = parameters(6)
d2 = 0
% Output equation.
y = [x(1)] % Displacement of the smaller mass
y = 50
x(2)
ans = 50
(-((k1+k2)*x(1))/m1) + ((k2*x(3))/m1) - (((d1+d2)*x(2))/m1) + ((d2*x(4))/m1) +u(1)
ans = -416.6667
x(4)
ans = 50
x(3)
ans = 50
x(4)
ans = 50
(d2*x(2)/m2) - (d2*x(4)/m2) + (k2*x(1)/m2) - (k2*x(3)/m2) + 0
ans = 0
(-((k1+k2)*x(1))/m1) + ((k2*x(3))/m1) - (((d1+d2)*x(2))/m1) + ((d2*x(4))/m1) +u(1)
ans = -416.6667
(d2*x(2)/m2) - (d2*x(4)/m2) + (k2*x(1)/m2) - (k2*x(3)/m2) + 0
ans = 0
% State equations.
dxdt = [x(2);(-((k1+k2)*x(1))/m1) + ((k2*x(3))/m1) - (((d1+d2)*x(2))/m1) + ((d2*x(4))/m1) + u(1);
x(4); (d2*x(2)/m2) - (d2*x(4)/m2) + (k2*x(1)/m2) - (k2*x(3)/m2) + 0]
dxdt = 4×1
50.0000 -416.6667 50.0000 0
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Mario Malic 2023 年 5 月 11 日

Oh my... I thought I was going crazy. I should take some time off. 😂
Thank you.
VBBV 2023 年 5 月 11 日

As you said, it works when parenthesis is added, it's again because of operator precedence. Parenthesis () operator has the higher precedence in equation than others, so when you add a () it then delineates everything within the outermost () as ONE expression or element in matrix and evaluates it, otherwise it's treated as 2 different elements

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