Consider two particles that experience a mutual force but no external forces. The classica...

Consider two particles that experience a mutual force but no external forces. The classical equation of motion for particle 1 is , and for particle 2 is  where the dot means a time derivative. Show that these are equivalent to

vcm = constant and vrol = Fmutual/µ

where vcm≡ (m1v1 + m2v2)/(m1 + m2\ Fmutual ≡ F1 on 2,m2 = -F2 on l-and

In other words, the motion can be analyzed in two pieces: the center of mass motion, at constant velocity; and the relative motion, but in terms of a one-particle equation where that particle experiences the mutual force and has the "reduced mass" µ.