What is you belly orbiting? :)

The reduced mass is like latej said, the effective mass but the correct term is reduced mass of two bodies. The reduced mass is the effective mass of your belly and something else and there is a center of mass between your belly and something else..

In TT it should be between the ball and paddle.

OK, read this zeio

https://en.wikipedia.org/wiki/Reduced_mass

The equation and derivation of reduced mass is simple.

Note that in the wikipedia page e is the coefficient of restitution. Stop trying to redefine it.

There is a formula for the change in kinetic energy in the collision of particles.

Some re-arranging and substituting needs to be done to calculate the speed of the paddle and ball after impact.

The equivalent using reduced mass results in the same answer as the speed after impact formula given the same inputs.

Normally reduced mass is used in orbital calculations. For instance the earth and the moon as seen by mars can be simplied by using the reduced mass of the earth and moon as one mass with the center of mass being between the center of the earth and the center of the moon.Doesn't reduced mass seem like overkill for determining the speed of a TT ball after impact?

Now where does zieo calculate the speed after impact using reduced mas? That formula hasn't been revealed yet.