Galilei invariance, action-reaction principle, and center of mass theorem

The Galilei invariance of classical dynamics does not automatically imply the third Newtonian axiom and the center of mass theorem. For the deduction of these theorems from Galilei invariance it is necessary to have, generally, a ''kinematical potential'' and a ''potential function'', respectively. In celestial mechanics it is possible to have conservation of the motion of the center of gravity but not of the mass center. In this case, the active and the passive masses are different quantities. (author)