Jacobi coordinates for three particles
= Jacobi coordinates for three particles
{c}
For three particles, choose the relative position of particles one and two, the position of their center of mass relative to particle three, and the total center of mass. The kinetic energy diagonalizes with masses
$$
\frac{m_1m_2}{m_1+m_2},
\qquad
\frac{(m_1+m_2)m_3}{m_1+m_2+m_3},
\qquad
m_1+m_2+m_3.
$$