2-Body Lagrangian problem

I have been looking at the problem of 2 point masses connected by a spring in polar coordinates. The problem is solved using the center of mass coordinate R and the relative coordinate r where M=total mass and m=reduced mass. The Euler-Lagrange equations then give equations for P(a vector) and p(subscript r) and L(which i think is p subscript θ). But i don't understand what these 3 quantities represent ?
Is it motion about the origin or the center of mass ? Is it in the radial direction ? p subscript r normally is but this time r is the relative coordinate , not necessarily radial.
Thanks