I was looking at the Wikipedia entry on the Hamilton-Jacobi equation, and was confounded by the equation at the beginning of the section on spherical coordinates:
http://en.wikipedia.org/wiki/Hamilto...al_coordinates
Shouldn't the Hamiltonian simply be
$$
H = \frac{1}{2m} \left[ p_r^2 + p_\theta^2 + p_\phi^2 \right] + U(r, \theta, \phi)
$$
?
http://en.wikipedia.org/wiki/Hamilto...al_coordinates
Shouldn't the Hamiltonian simply be
$$
H = \frac{1}{2m} \left[ p_r^2 + p_\theta^2 + p_\phi^2 \right] + U(r, \theta, \phi)
$$
?