How to get the jacobian of a symbolic vector?
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Hi,
The following code uses diff(X) and jacobian(r,X) in order to get velocity and accelaration of a point. However, this error appears when I try run:
"Error using sym/jacobian (line 44)
The second argument must be a vector of variables."
t is a variable (time), Phi, Theta and R are functions of t, X is a vector using Phi, Theta and R,(position of the point in cylindrical coordenates) r is function of Phi, Theta and R (position of a point in the cartesian coordenates).
syms t
Phi=sym('Phi(t)');
Theta=sym('Theta(t)');
R=sym('R(t)');
X = [Phi, Theta, R].'
dXdt=diff(X);
d2Xdt2=diff(dXdT);
r = [R*cos(Phi)*sin(Theta), R*sin(Phi)*sin(Theta), R*cos(Theta)].' %position
Ht = jacobian (r,X) %jacobian
vt=Ht*dXdt %velocity
at=Ht*d2Xdt2+diff(Ht,t)*dXdt %acceleration
=========================================================
It's strange, because the "jacobian(r,X)" works very well in the following code:
syms Phi Theta R
X = [Phi Theta R].';
r = [R*cos(Phi)*sin(Theta), R*sin(Phi)*sin(Theta), R*cos(Theta)].'
jacobian(r,X)
In this case, I can't get dXdt, but when Phi, Theta and R are functions of t, I can't get the jacobian :/
2 Comments
John D'Errico
on 21 Mar 2015
Use the "{} Code" button to format your code. Otherwise, it shows as an unreadable mess.
Answers (1)
John D'Errico
on 21 Mar 2015
Note that in your code, you have the lines...
dXdt=diff(X);
d2Xdt2=diff(dXdT);
MATLAB gets upset here, because you can't type. It gives the error message:
Undefined function or variable 'dXdT'.
You never defined dXdT, only dXdt.
Next, the error you get reflects a problem in your code. You have defined the FUNCTIONS, Theta, Phi and R, as parametric functions of t. They are not variables. The only variable in this is t.
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