The global controllability of some mechanical systems with absolutely elastic impacts

Sufficient conditions are presented for the stabilizability and global controllability of certain natural Lagrangian systems with a non-negative potential energy when there are ideal unilateral constraints. In the general case, the number of controls is less than the number of degrees of freedom and the controls are bounded by preassigned quantities. Examples of globally controlled systems with two degrees of freedom are considered in which the action of the unilateral constraints is modelled within the framework of classical collision theory.