Substitute a differential expression for a variable subs()

I want to substitute in the following matrix result: A=[diff(theta(t),t) -diff(psi(t),t); -diff(theta(t),t) diff(psi(t),t)] I want to substitute diff(theta(t),t) for a variable called thetap and diff(psi(t),t) for a variable called psip in orden to obtain the following matrix A=[thetap -psip -thetap psip]

then I tried to do this:

theta2 = sym('theta2(t)') psi2 = sym('psi2(t)'

A=[diff(theta(t),t) -diff(psi(t),t); -diff(theta(t),t) diff(psi(t),t)]

dtheta = diff(theta,t) dpsi = diff(psi,t)

Ap_s = subs(A,{dtheta,dpsi},{thetap,psip})

but it doesn't work. It returns again the dependent expression diff(theta(t),t) and diff(psi(t),t) without doing the substitution. I've tried: Ap_s = subs(A,{diff(theta(t),t),diff(psi(t),t)},{thetap,psip}) but it doesn't work. Can anybody help me?

Answer 1

[Adarsh]

Hi @Mario Miralles Delgado,

Upon observing the given code, I have understood that you are trying to substitute the differential expressions in the matrix with shorter & new symbols.

I have found a workaround for the task which you are trying to accomplish, in the MATLAB documentation I have found a function named “str2sym” which converts the string version of a symbolic expression to original symbolic expression type.

Using this function, the expressions which are to be replaced can be given as input to the “subs” function as a cell array of symbolic types as shown here:

syms theta(t) t psi(t)
A=[diff(theta(t),t) -diff(psi(t),t); -diff(theta(t),t) diff(psi(t),t)] % Initial given matrix where substitution has to be done.

A = 

theta2 = str2sym('theta2(t)')

theta2 = 

psi2 = str2sym('psi2(t)')

psi2 = 

subs(A,{str2sym("diff(theta(t),t)"),str2sym("diff(psi(t),t)")},{theta2,psi2})% Using str2sym function to convert strings to symbolic expressions and pass them into subs as argument.

ans = 

by using this the required substitutions can be performed correctly as required.

Here is the link for the MATLAB documentation stating the usage of “str2sym” and “subs” functions :

1. https://www.mathworks.com/help/symbolic/str2sym.html
2. https://www.mathworks.com/help/symbolic/sym.subs.html

I hope this helps in achieving the desired output.