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. Begin by showing that the motion must lie in a plane so that the phase space is four dimensional (r, θ, pr, pθ, but only the first three are nontrivial). Calculate the projection of the phase path on the r-pr plane, then take into account the variation with θ.