Yes. It just a repetition of the same motion. However, it is not because I repeat the simulation. I did not do that.
It is just happened that the ball will move betwen topspin and backspin.
Before the first bounce: R*w>v , Let ?=R*w-v.
After the first bounce: v'= v+(4/5)(R*w-v) and w'=w-(6/5)(w-v/R);
If we calculate the new difference ?'=R*w'-v'= R*w-(6/5)(Rw-v) - v-(4/5)(R*w-v)=-(R*w-v)=-?
So after the second bonce, the relative velocity is reversed.
I will try to add more information and features according to your post : [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=719.msg2631#msg2631]Re: ping-pong spinny ball dynamics after bounce[/url]