 Center-of-mass coordinates

In the two-body problem, these coordinates separate the common translation from the internal separation. For total mass $M$ and reduced mass $\mu$, the kinetic energy is $M{\dot{R}}^2/2+\mu {\dot{r}}^2/2$. The conjugate momenta are $P=M\dot{R}$ and $p=\mu \dot{r}$ for the ordinary Newtonian kinetic term.