On averaging in systems with a variable number of degrees of freedom

Abstract An averaging procedure is established for systems with a variable number of degrees of freedom which arise when considering vibrocollisional oscillations with zero velocity restitution coefficient. Compared with the method of staged integration /1, 2/ the approach presented, associated with non-analytical changes in the variables /3, 4/, widens the class of systems that can be considered. Unlike the classical averaging method /5–7/ there is a reduction in the degenerate degrees of freedom because of the specific degeneracy of the problem.