two masses m 1 and m 2 move in a uniform gravitational field g and interact problems for chapter 8 321 via a potential energy u(r). (a) show that the lagrangian can be decomposed as in (8.13). (b) write down lagrange's equations for the three cm coordinates x, y, z and describe the motion of the cm. write down the three lagrange equations for the relative coordinates and show clearly that the motion of r is the same as that of a single particle of mass equal to the reduced mass it, with position r and potential energy u(r).