26. (i) For Newton's equation it + $(1 :13) = 0, nd the potential energy U (2:), the kinetic energy, as well as the Lagrangian. What are the equilibrium points for this equation? (ii) Multiply Newton's equation in part (i) by :i: and integrate to obtain the total energy, E. Sketch U (x), and use it and E to sketch the trajectories of the equation in the x-iplane. (iii) Extra credit: What is the value of the energy along the separatrix loop