Center-of-mass coordinates
= Center-of-mass coordinates
{title2=$R=(m_1r_1+m_2r_2)/(m_1+m_2),\quad r=r_1-r_2$}
= Centre-of-mass coordinates
{synonym}
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.