Set up the problem of the spherical pendulum in the Hamiltonian formulation, using spheric...

Set up the problem of the spherical pendulum in the Hamiltonian formulation, using spherical polar coordinates for the qi. Evaluate directly in terms of these canonical variables the following Poisson brackets:

showing that they have the values predicted by Eq. (9.128). Why is it that pθ and pψ, can be used as canonical momenta, although they are perpendicular components of the angular momentum?