Problem 1 A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. The two pendula have equal lengths l, bobs of equal mass m. and are conned to move on the .r 3; plane. Write down the Lagrangian in terms of the generalized coordinates 8 and 0 and derive the corresponding Euler-Lagrange equations. (9 and o are the angles the upper and lower pendulum make with the downward vertical respectively)