13.5** A bead of mass m is threaded on a frictionless wire that is bent into a helix with cylindrical polar coordinates (p, o, z) satisfying z = co and p = R, with c and R constants. The z axis points vertically up and gravity vertically down. Using as your generalized coordinate, write down the kinetic and potential energies, and hence the Hamiltonian H as a function of and its conjugate momentum p. Write down Hamilton's equations and solve for and hence z. Explain your result in terms of Newtonian mechanics and discuss the special case that R = 0.

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