Jacobian Matix vector of variables?

Hello, im want to get a jacobian from this code

syms x(t) y(t) z(t);
syms u(t) v(t) w(t);
syms p(t) q(t) r(t);
syms phi(t) theta(t) psi(t);

 x_p=w(t)*(sin(phi(t))*sin(psi(t)) + cos(phi(t))*cos(psi(t))*sin(theta(t))) - v(t)*(cos(phi(t))*sin(psi(t)) - cos(psi(t))*sin(phi(t))*sin(theta(t))) + cos(psi(t))*cos(theta(t))*u(t);
   y_p=v(t)*(cos(phi(t))*cos(psi(t)) + sin(phi(t))*sin(psi(t))*sin(theta(t))) - w(t)*(cos(psi(t))*sin(phi(t)) - cos(phi(t))*sin(psi(t))*sin(theta(t))) + cos(theta(t))*sin(psi(t))*u(t) ;
   z_p=cos(phi(t))*cos(theta(t))*w(t) - sin(theta(t))*u(t) + cos(theta(t))*sin(phi(t))*v(t);
V=[x_p,y_p,z_p];
   a=[x y z];
AP=jacobian(V,a)

That my error massage

Error using sym/jacobian (line 44)

Second argument must be a vector of variables.

Can someone pls explain to me,whats causing the problem?

Answer 1

[Stephan]

You have to distinguish between a symbolic variable

syms x

and a symbolic function

syms y(t)

This is why this works:

syms rho phi x y z
V = [3*phi*x^2+y; 2*rho/x*y; -x; 3*y]
a=[x y]
AP=jacobian(V,a)
 
V =
 
 3*phi*x^2 + y
   (2*rho*y)/x
            -x
           3*y
 
 
a =
 
[ x, y]
 
 
AP =
 
[        6*phi*x,         1]
[ -(2*rho*y)/x^2, (2*rho)/x]
[             -1,         0]
[              0,         3]

and your code does not. The second Input argument to jacobian have to be symbolic variables, not symbolic functions.