An action integral is presented for Hamiltonian mechanics in canonical form with unilateral constraints and/or impacts. The transition conditions on generalized impulses and the energy are presented as variational inequalities, which are obtained by the application of discontinuous transversality conditions. The energetical behavior for elastic, plastic and blocking type impacts are analyzed. A general impact equation is obtained by the stationarity conditions, which is compatible with the most general impact laws and is applicable to various impactive processes straightforwardly. The crux in achieving energetical behaviour which conforms with the physics of the impactive process, is shown to be the consistency conditions on the impact time variations.
Journal of Nonlinear Science JNLS-D-14-00106 submitted., 10.5.2014