Problem 3) Two masses m, and m2 move under their mutual gravitational attraction in a uniform external gravita- tional field whose acceleration is g. Choose as coordinates the Cartesian coordinates X, Y, Z of the cen- ter of mass vector R (taking Z in the direction of g) and the spherical coordinates r, and that define the relative vector r from m; and m2 (see HW Problem Set 1 for the definition of r). Write down the Lagrangian in terms of these 6 coordinates. Calculate all 6 generalized momenta. Which of these 6 momenta is conserved? Write down the 6 Euler-Lagrange equations of motion.