MATLAB: How can i differentiate diff(q(t), t) again

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Hello..

I started to compute a function which has a variable depending on time which I defined as q(t). In the computation, the variable was differentiated and I ended up with diff(q(t), t). Now I want to further differentiate this resulting function wrt diff(q(t), t) i.e. q' but when I wrote "diff(exp3, diff(q(t), t));" matlab showed an error: "Second argument must be a variable or a nonnegative integer specifying the number of differentiations".

Can anybody help me figure this out.

So far I have tried to use functionalDerivative but that doesnt seem to work as well. Also I have found a way around this: I can use the sub function to substitute diff(q(t), t)) by qdot and do this diff(exp3, qdot); but that isnt what I intend to do.

Please Help.

Best Answer

You cannot differentiate with respect to a function in normal calculus, only with respect to a variable. Differentiating with respect to a function requires Calculus of Variations.

People often propose that you substitute a variable for the function and differentiate with respect to that. However a number of years ago I posted an example of a case where that would produce the wrong answer. Unfortunately it was long enough ago that it would be difficult to find the post.

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MATLAB: Mupad partial time derivative

You substitute s for q(t), so B transforms into s*diff(s,t) . s is constant with respect to t so diff(s,t) is 0 and s*0 is 0 (provided that s is finite) so s*diff(s,t) is going to collapse to 0. Then you take the derivative of that 0 with respect to s, which is going to be 0.

MATLAB: Derivative of a symbolic function with multiple dependent variables

If you want to substitute values for q(t) and dq(t), you may fisrt substitute the value for dq(t) followed by the value for q(t). Let the value to be substituted for dq(t) be 2.

syms q(t)
f = 2*q^2;
fd = diff(f,t)
a = subs(fd,diff(q(t),t),2)

which gives an output

fd(t) = 4*q(t)*diff(q(t), t)
a(t) = 8*q(t)

Now, you may substitute the value of q(t) in a(t)

subs(a(t),q(t),5)

to get the ouput as

ans = 40

Best Answer

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MATLAB: Mupad partial time derivative

MATLAB: Derivative of a symbolic function with multiple dependent variables

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