How to define a dependent variable for differentiaion?

Hi,

I have a variable A which is dependent on x, but I don't know the expression yet.

I have a differential equation dA/dx which is given as

dA_x = (T*b-E*Q*diff(C_s,x))/(E*S);

All the entities except C_s are constants. I can get A by integrating this equation.

A = int(dA_x,x);

But the problem lies with the differential expression of C_s which is given by

C_s = (M-2*A*E*Q)/(2*E*I);

Since A is not yet defined as a function or dependent variable of x, the differentiation results in 0.

How do I solve this?

I'm not looking for a numeriacal answer, I just need a symbolic expression.

Answer 1

[Ameer Hamza]

Define symbolic variable A like this

syms A(x)

It will tell MATLAB that a depends on x and will not become zero on differentiation.

[Abinav]

Thanks. That worked.

[Ameer Hamza]

I am glad to be of help!

[Abinav]

That's solved. But now I have A(x) on both sides of the equation and substituting it in other equations results in a continuous substitution loop.

[Ameer Hamza]

Can you show an example? What is the issue?

[Abinav]

syms L b h S I Q E u F M T c theta w k
syms x A(x) dA_x C_s(x)

S = b*h;        
I = b*h^3/3;    
Q = b*h^2/2;

M = -((F*L^2)/2)+(F*(L*x-x^2/2));

C_s = (M-2*A*E*Q)/(2*E*I);
dA_x = (T*b-E*Q*diff(C_s,x))/(E*S);
A = int(dA_x,x);

At this point, the diff(C_s,x) becomes C_s. And matlab makes a substitution from the above equation resulting in A(x) on both sides of equation. Which is mathematically correct.

C_s = subs(C_s,A)

But when I substitute A back into my C_s, there is still an A term in the equation. This could be avoided if matlab retains keeps the term as C_s while integrating instead of substituing the equation in there.

In either case, the problem can be solved by rearranging the terms but I can't figure out a way to do that in Matlab.

[Ameer Hamza]

Symbolic variables can be a bit confusing sometimes. For this case, the following code will work

syms L b h S I Q E u F M T c theta w k
syms x A(x) dA_x(x) C_s(x)
S = b*h;        
I = b*h^3/3;    
Q = b*h^2/2;
M = -((F*L^2)/2)+(F*(L*x-x^2/2));
C_s = (M-2*A*E*Q)/(2*E*I);
dA_x = (T*b-E*Q*diff(C_s,x))/(E*S);
A = int(dA_x,x);

C_s = subs(C_s);