The bouncing motion of a superball between a horizontal floor and a vertical wall

In earlier work [P.J. Aston, R. Shail, The dynamics of a bouncing superball with spin, Dyn. Sys. 22 (2007) 291–322] the problem of the possible back and forth motion of a superball thrown spinning onto a horizontal plane was considered in detail. In this paper the problem is extended to include a vertical wall. In particular motion of the superball where it bounces alternately on the floor and the wall several times is considered. Using the same physical model as in our previous work, a non-linear mapping is derived which relates the launch data of the (n+1)th floor bounce to that of the n th. This mapping is analysed both numerically and theoretically, and a detailed description is presented of various possible motions. Regions of initial conditions which result in a specified number of bounces against the wall are also considered.