To simplify my question I would like to use a random example (although, the issue holds regardless of the numbers you pick). Suppose two objects collide (head-on) in one dimension. The initial parameters are as follows (units are irrelevant): m1=1;m2=2;u1=3;u2=-4; Also, suppose that exactly 90% of the KE is lost as a result of the collision (hence, the coefficient of restitution is sqrt(0.9)). Now I can convert both velocities into the center-of-mass frame of reference, invert them, multiply by sqrt(0.9) and convert back into the lab frame of reference to get (one of the two solutions): v1=-6.09384 and v2=-0.54692 The problem with these numbers is: if I keep everything in the lab frame of reference and plug all these numbers into these equations (where ε=0.9): their LHS is not equal to their RHS by quite a significant quantity. What am I missing? Thanks!