Consider a 3d particle in terms of polar spherical coordinates 'F' = (739, ). (a) Write down the Lagrangian and derive the expression for the Hamiltonian. (b) Let E denote the angular momentum, express E2 in terms of the same canonical variables as in the Hamiltonian H. (c) From (a) and (b) deduce the form of the energy E in terms of r, pr, and E2