2. Conserve some quantities A physical system with 2 generalized coordinates (x and 6) is described by the Lagrangian L = MR²¢² + ½(M + m)i² - mgl cos p. (a)

Write down the two Euler-Lagrange equations. Calculate the partial derivatives, but do not solve the resulting differential equations. (b) Find a quantity that is conserved (M, m, l, and R are not valid answers). Do you recognize what that quantity is? (c) Find another conserved quantity. What is that quantity?