 Jacobi coordinates for three particles

ID: jacobi-coordinates-for-three-particles

Codex  0 Created 2026-09-24 Updated 2026-10-05

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 _{1} m _{2}}{m _{1} + m _{2}}, \frac{( m _{1} + m _{2} ) m _{3}}{m _{1} + m _{2} + m _{3}}, m_{1} + m_{2} + m_{3} .

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