How do I solve for the Hamilton-Jacobi equation in a spherical forcefield?

[FichaG]

Homework Statement

A particle of mass m moves in the forcefield whose potential in spherical coordinates is V= - (K cos θ)/r²
Whrite the Hamilton-Jacobi equation describing its motion.

Homework Equations

H=(p_r² / 2m)+ (p_θ² / 2mr²)+(p_φ² / 2mr²sin ²θ) + V

The Attempt at a Solution

I don't know how to do it because it's the first exercise of its kind to I have to solve

 

[theodoros.mihos]

If kinetic energy is $T(\dot{x}_i)$ only and potential energy is $V(x_i)$ only, then:
$$ \frac{d\mathbf{p}_i}{dt} = -\frac{\partial{U}}{\partial{x}_i} $$
and think about what is the partial derivation on some direction. U is the potential energy.