center-of-momentum frame

Thus "center of momentum" already means "center-of-momentum frame" and is a short form of this phrase.

This frame is also called the center-of-mass frame, or center-of-momentum frame.

In the center-of-momentum frame (COM frame), by definition we have:

A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a physical point) is at the origin at all times.

Even if we consider the same system from center-of-momentum frame, where net momentum is zero, the magnitude of the system's invariant mass is not equal to the sum of the rest masses of the particles within it.

The center-of-momentum frame is notable for being the reference frame in which the total energy (total relativistic energy) of a particle or compound object, is also the invariant mass (times the scale-factor speed of light squared).

Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed.