How to find the time and partial derivative?

Hello!

I have this:

How to represent the above in matlab in order to find the partial derivative w.r.t. q1_dot, that is the below

And after that i want to find the time derivative from the above.

Thanks in advance

[Walter Roberson]

Is q1_dot the same as diff(q1) ? That is, are you trying to find a partial derivative with respect to a derivative? Or is q1_dot just an unusual variable name? Or is it an unusual function name ?

[RoBoTBoY]

Yes q1_dot is the diff(q1(t))

[RoBoTBoY]

syms q1(t) q2(t) l1 l2 m I
K = 1/2*m*diff(q1(t),t)^2+1/2*(m*l2^2+I)*diff(q2(t),t)^2-m*diff(q1(t),t)*l2*sin(q2)*diff(q2(t),t)
diff(K,t)

I tried the above in live script but I'm not sure

[Walter Roberson]

syms q1(t) q2(t) l1 l2 m I
K = 1/2*m*diff(q1(t),t)^2+1/2*(m*l2^2+I)*diff(q2(t),t)^2-m*diff(q1(t),t)*l2*sin(q2)*diff(q2(t),t)

K(t) = 

That does seem to be the same as your equatiom

diff(K,t)

ans(t) = 

This is, however, not the same as diff(K,q1_dot)

syms Q1_dot
Ks = subs(K(t), diff(q1), Q1_dot)

Ks = 

diff(Ks, Q1_dot)

ans = 

[RoBoTBoY]

Ok, I think it's same with yours

[RoBoTBoY]

But how to find the second part of my question, that is the time derivative?

[RoBoTBoY]

Maybe this?

[Walter Roberson]

syms q1(t) q2(t) l1 l2 m I
K = 1/2*m*diff(q1(t),t)^2+1/2*(m*l2^2+I)*diff(q2(t),t)^2-m*diff(q1(t),t)*l2*sin(q2)*diff(q2(t),t)

K(t) = 

syms Q1_dot
Ks = subs(K(t), diff(q1), Q1_dot)

Ks = 

dK_q1_dot = diff(Ks, Q1_dot)

dK_q1_dot = 

dK_q1_dot_dt = diff(dK_q1_dot, t)

dK_q1_dot_dt = 

Answer 1

[Alan Stevens]

You don't really need the power of MATLAB here; elementary calculus will do:

[RoBoTBoY]

Yes indeed, but i want the power of MATLAB to verify my maths.