A three-dimensional map is studied in this paper to provide a fundamental understanding for
the vibro-impact capsule system, which is a non-autonomous two degrees-of-freedom non-
smooth dynamical system consisting of soft impact and dry friction with forward and
backward drifts. By using the map, one can investigate the global and local dynamics of the
system and construct all possible local mappings for a wide range of parameter variation. An
example study by varying the amplitude of external excitation of the system is presented. Our …