Symbolic math- substitute a derivative function with subs()?

Hello everyone,

I've got a symbolic derivative :

 syms J phi(t) Ja J0 x1 x2
  J=J0-Ja*cos(2*phi);
  dJ=diff(J)

This yields:

dJ(t)=2*Ja*D(phi)(t)*sin(2*phi(t))

Now, in this function I want to substitute phi(t) for x1 and D(phi)(t) for x2.

subs(dJ(t),phi,x1)

ans =

2*Ja*D(phi)(t)*sin(2*x1)

but this doesnt work for D(phi)(t)

>> subs(dJ(t),D(phi)(t),x2)
Error: ()-indexing must appear last in an index expression.

>> subs(dJ(t),D(phi),x2)
Undefined function 'D' for input arguments of type 'symfun'.

>> subs(dJ(t),D(phi(t)),x2)
Undefined function 'D' for input arguments of type 'sym'.

How could it be substituted by x2?

Answer 1

[Andrew Horchler]

A late answer, but maybe this will help others. See my answer here on StackOverflow.com/Matlab. In this case you can substitute both variable at once via:

syms phi(t) Ja J0 x1 x2
J = J0-Ja*cos(2*phi);
dJ = diff(J,t)
dphi = diff(phi,t)
subs(dJ,{phi,dphi},{x1,x2})

You also don't need to define J as symbolic using syms since it gets allocated as such when you create the equation. I do usually like to make explicit the variable that I'm differentiating with respect to as well.

Answer 2

[Kobi]

why don't you sub one char at a time?

[Maria Perdomo]

Thats what I do, the problem is the syntaxis for

   D(phi)(t)

that is a derivative function

[Maria Perdomo]

I do one at a time, you see it works for phi(t):

dJ(t)=2*Ja*D(phi)(t)*sin(2*phi(t))

subs(dJ(t),phi,x1)

ans =
2*Ja*D(phi)(t)*sin(2*x1)

Answer 3

[Walter Roberson]

syms x3
subs( subs(dJ(t),D(phi),x3), x3(t), x2 )

[Maria Perdomo]

syms J phi(t) Ja J0 x1 x2 x3
J=J0-Ja*cos(2*phi);
dJ=diff(J);
subs( subs(dJ(t),D(phi),x3), x3(t), x2 )

>>Undefined function 'D' for input arguments of type 'symfun'.

[Walter Roberson]

subs( subs(dJ(t),sym('D(phi)'),x3), x3(t), x2 )