* The kinetic energy of the center of mass in the center of mass frame is zero since the center of mass is at rest in the cm-frame.

* The total kinetic energy in the lab frame is equal to the kinetic energy of the center of mass plus the kinetic energy of the particles relative to the center of mass.

* The total kinetic energy of a system of particles can never be less than the kinetic energy of its center of mass. This means that the maximum energy that can be lost during any collision is equal to the kinetic energy of the particles relative to the center of mass.

* The energy loss in any one-dimensional collision can be expressed as function of the coefficient of restitution and the kinetic energy of the particles relative to the center of mass. Derivation.