Assume that the Lagrangian is a polynomial in of no higher order than quadratic. Convert...

Assume that the Lagrangian is a polynomial in of no higher order than quadratic. Convert the 2n equations (8.2) and (8.14)

into 2n equations for and in terms of q and p, using the matrix form of the Lagrangian. Show that these are the same equations as would be obtained from Hamilton’s equations of motion.