Symbolic Math Toolbox - Derive a function with respect to another function

Hello,

i want to verify a calculation I did already on paper. There the following problem occurs:

>> clear all
>> syms t x(t)
>> f=3*x
>> diff(f,x)
Error using sym/diff (line 26)
All arguments, except for the first one, must not be symbolic functions.

I want to derive a funtion woth respect to another function of time. And i even need the derivation of a function with respect to another derivative of a function of time.

I need this because I want to get the equations of motion of a system by using Lagrange equations of the second kind .

Can anybody help me with this problem? Thanks a lot. Johannes

Answer 1

[Zoltán Csáti]

I also bumped into this question when I wanted to create the equation of motion using this method. Matlab's Symbolic Math Toolbox uses the Maple engine, so you can try the following: Physics:diff(L(t), ydot(t)), where L(t) is the Lagrangian that you want to differentiate with respect to the time derivative of coordinate y(t). I stress again, that this code is in Maple. As I see from your error message, it can't be done in Matlab. Therefore use Maple or do it by hand.

[mistajojo]

I found solve it in matlab. Maybe it's not the best way, but it works anyway. The solution is to substitute x(t) by another variable. I built a own function which does this:

function [f_out] = diff2(f_in,ableiten)

syms substitute;
f_zwischen=subs(f_in,ableiten,substitute);
f_zwischen_diff=diff(f_zwischen,substitute);
f_out=subs(f_zwischen_diff,substitute,ableiten);
end

But be careful. For some reason it only works properly if it is typed like this:

diff2(f,x(t))

If it is typed like the following statement it wont work properly !

diff2(f,x)

[Zoltán Csáti]

Thanks.

Answer 2

[Joan Sans]

it works perfect! Thanks