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How do you take the partial derivative of a function relative to theta dot

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Need to take the partial derivative of l with respect to theta 1 dot
clear; clc;
syms theta1(t) theta2(t) r1 r2 m1 m2 g
%theta1dot=diff(theta1)
%theta2dot=diff(theta2)
x1 = r1*sin(theta1);
y1 = -r1*cos(theta1);
x2 = x1+r2*sin(theta2+theta1);
y2 = y1-r2*cos(theta2+theta1);
x1dot=diff(x1)
y1dot=diff(y1);
x2dot=diff(x2);
y2dot=diff(y2);
pe=m1*g*y1+m2*g*y2;
ke=1/2*m1*(x1dot^2+y1dot^2)+1/2*m2*(x2dot^2+y2dot^2);
l=ke-pe
diff(l,theta1)

Accepted Answer

Andreas Apostolatos
Andreas Apostolatos on 29 Nov 2022
Edited: Andreas Apostolatos on 29 Nov 2022
Hi Cason,
You can achieve this workflow by substituting the symbolic expression diff(theta1) with a symbolic variable theta1dot in expression l(t), take the derivative of that expression with respect to theta1dot and finally substitute back symbolic variable theta1dot with diff(theta1) in the resulting expression, namely,
syms theta1dot
subs(diff(subs(l(t), diff(theta1(t)), theta1dot), theta1dot), theta1dot, diff(theta1(t)))
I have cascaded all underlying operations, but feel free to expand them in multiple lines of code to get a more readable version of the latter one. For more information on function subs, please read the corresponding documentation page,
I hope this helps.
Kind regards
Andreas

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