Consider a particle moving in a potential U(r). Rewrite the Lagrangian in terms of a coordinate system in uniform rotation with respect to an inertial frame. Calculate the Hamiltonian and determine whether H = E. Is H a constant of the motion? If E is not a constant of motion, why isn’t it? The expression for the Hamiltonian thus obtained is the standard formula ½ mv2 + U plus and additional term. Show that the extra term is the centrifugal potential energy. Use the Lagrangian you obtained to reproduce the equations of motion given in Equation 10.25 (without the second and third terms).