A system is described by the single (generalized) coordinate q and the Lagrangian L (q,(q·)). Define the generalized momentum associated with q and the corresponding Hamiltonian, H (q , p). Derive Hamilton's equations from Lagrange's equations of the system. For the remainder of the question, consider the system whose Lagrangian, L (q,(q·)). Find the corresponding Hamiltonian and write down Hamilton's equations.