classical mechanics - Numerical torque calculation

Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically compute force acting on the center of mass of the body by calculating numerical derivatives e.g. $F_x = (E(x + dx) - E(x - dx)) / (2 * dx)$. But if you do the same for Euler angles this doesn't give you torques. So how do I convert numerical derivatives of energy by Euler angles to the resulting torque on a body?

Answer

OK. I found the answer:

$$\partial V/\partial \theta = N_x \cos \psi - N_y \sin \psi$$ $$\partial V/\partial \phi = N_x \sin \theta \sin \psi + N_y \sin \theta \cos \psi + N_z \cos \theta$$ $$\partial V/\partial \psi = N_z$$

Where $\theta, \psi, \phi$ are Euler angles and $N_x, N_y, N_z$ are Torque components.