The method of direct separation of motions and the general approach, called by the author "vibrational mechanics", is developed so as to fit the problems of the effect of vibration on systems with dry friction and shock. The main idea of this approach lies in the transfer from the initial system of differential equations to the system, describing only the slow components of motion, most interesting for applications. It is these equations that are called the equations of vibrational mechanics. The advantages of this approach are especially significant in the case of systems with dry friction (Coulomb friction) and with unilateral constraints whose presence in case of vibration leads to multiple collisions of the system bodies. Instead of the not smooth system or with the discontinuous right sides there is a "smooth" system often of a lower order; an essentially non-potential system may be answered by a potential system.
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