# Homework Help: Hamilton-Jacobi Equation

1. May 30, 2015

### FichaG

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
H=(pr2 / 2m)+ (pθ2 / 2mr2)+(pφ2 / 2mr2sin 2θ) + V

3. 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

2. May 30, 2015

### 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.