The Lagrangian for a system of one degree of freedom can be written: L = m 2 (q_2sin2!t + q_q!sin2!t + q2!2): a) What is the corresponding Hamiltonian? Is it conserved? b) Introduce a new coordinate de ned by Q = qsin!t. Find the

(a) Find the equations of motion by using Lagrange's equation and interpret the equations by giving a physical interpretation of the forces acting on the particle. (c) Find the canonical momentum and construct the Hamiltonian. Is this Hamiltonian a constant of the motion? (d) Introduce a new coordinate defined by Q = q sin omega t. Find the Lagrangian in terms of the new coordinate and the corresponding Hamiltonian. Is this new Hamiltonian a constant of the motion?