= 1. Consider a mass m moving under the influence of a central potential U - +. From first principles, construct the Hamiltonian in terms of the action variables I, and Io. The use of complex methods is optional, and is probably easier. Using the action-angle formulation, show that Tr=To only when k = 0. Based on the action-angle description, sketch the motion when ky> 0 and provide quantitative evidence for the sketch, Finally, for what values of k, will the system exhibits N revolutions about the origin in the same time that it undergoes M oscillations in r?