Changing a symbolic differentiation term to a variable.

The issue I have ran into is that I have taken a symbolic derivative and I am hoping to simpliy the naming format. This is a sample of the code that I am doing currently and the output I am getting.

Input:

syms t phi(t)
phi = phi(t);
M        = [cos(phi) (-sin(phi)) 0
           sin(phi) cos(phi)    0
           0        0           1];
           
M_dot = diff(M,t)

Output:

M_dot =
 
[ -sin(phi(t))*diff(phi(t), t), -cos(phi(t))*diff(phi(t), t), 0]
[  cos(phi(t))*diff(phi(t), t), -sin(phi(t))*diff(phi(t), t), 0]
[                            0,                            0, 0]

My goal is to be able to rename the "diff(phi(t),t)" so that it simplifies my longer matrices. I have tried the subs(s, new, old) function and it returned an error so I need to find a different way.

Let me know what you all think. Thank you.

[Walter Roberson]

I think you mean diff(M,t) not diff(R1,t)

Answer 1

[Walter Roberson]

syms dphi_dt
subs(M_dot, diff(phi), dphi_dt)

However, if you have multiple derivative levels, this will not find them. For example if you had diff(phi,t,t) then this would leave that alone rather than constructing diff(dphi_dt,t) or diff(dphi_dt(t),t)

Also, be careful: differentiating the result with respect to t will treat dphi_dt as a constant unless you do

syms dphi_dt(t))
subs(M_dot, diff(phi), dphi_dt)