A one-degree-of-freedom mechanical system is described by the foIlowing Lagrangian: L(Q, Q, t) = cos² øt 2 - QQ sin 2ot – cos 2wt . 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe?

A one-degree-of-freedom mechanical system is described by the foIlowing Lagrangian: L(Q, Q, t) = cos² øt 2 - QQ sin 2ot – cos 2wt . 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe?