The problem of the existence and stability of periodic and almost periodic solutions of strongly non-linear impulsive systems is investigated. The Poincaré method [1] is justified for the case of an isolated generating solution. A dynamical system consisting of a bead on a vibrating surface is considered as an example. The small parameter method for investigating systems with discontinuous solutions was previously applied [2, 3] to the case when the periodic solution is non-isolated. A method is used below for reducing the investigation of a system of equations with impulsive actions on surfaces to equations with fixed moments of inpulsive action. |