A particle moves in a spherically symmetric force field with potential energy given by U(r) = – k/r. Calculate the Hamiltonian function in spherical coordinates, and obtain the canonical equations of motion. Sketch the path that a representative point for the system would follow on a surface H = constant in phase space is four dimensional (r, θ, p, pФ, but only the first three are nontrivial). Calculate the projection of the phase path on the r-p, plane then take into account the variation with θ.