Assigning values to defined symbolic variables afterwards

syms x ar la 


C_I=[((1+(4/3)*ar*sin(x))/8)*la,0,0,0;0,((1-(4/3)*ar*cos(x))/8)*la,0,0; 0,0,((1-(4/3)*ar*sin(x))/8)*la,0; 0,0,0,((1+(4/3)*ar*cos(x))/8)*la];
Lb=[1,-1,cos(x),sin(x);1,1,sin(x),-cos(x);1,-1,-cos(x),-sin(x);1,1,-sin(x),cos(x)];

Lb_1=inv(Lb);

Cm=Lb_1*(2*(diff(Lb,x))+(C_I*Lb));

How can you calculate the Cm matris while x=0 ? What code should I write next?

Answer 1

[Star Strider]

Use the subs funciton (and optionally simplify).

Try this —

syms x ar la 
sympref('AbbreviateOutput',false);
C_I=[((1+(4/3)*ar*sin(x))/8)*la,0,0,0;0,((1-(4/3)*ar*cos(x))/8)*la,0,0; 0,0,((1-(4/3)*ar*sin(x))/8)*la,0; 0,0,0,((1+(4/3)*ar*cos(x))/8)*la]

C_I = 

Lb=[1,-1,cos(x),sin(x);1,1,sin(x),-cos(x);1,-1,-cos(x),-sin(x);1,1,-sin(x),cos(x)]

Lb = 

Lb_1=inv(Lb)

Lb_1 = 

Cm=Lb_1*(2*(diff(Lb,x))+(C_I*Lb))

Cm = 

Cm_x0 = subs(Cm,{x},{0})                                    % Substitute 0 for 'x'

Cm_x0 = 

Cm_x0 = simplify(Cm_x0, 500)                                % Simplified

Cm_x0 = 

.

[Alexi]

thanks

[Star Strider]

As always, my pleasure!

[Alexi]

I have one more question, sir. There is a difference in only one cell (4th row, 2nd column) between the final matrix obtained from the source I refer to and the matrix (cm_x0) that I found by applying the same operations, is it because of the mathematical difficulty? because I do not think that a single error is caused by formulations.( For simplicity, you can take ar and la as 1, their equivalents here are gamma and mu.)

[Torsten]

Same difference also in 2nd row, 4th column.

[Star Strider]

The μ and γ are new.

How are they defined, especially in the context of the other variables?

[Alexi]

μ=ar γ=la