Averaging method applicable to the dynamics of not fully elastic bodies

Abstract

Using well-known methods, various problems of dynamics are reduced to a standard system of integral differential equations, accounting for heredity effects in the form of multiple integrals according to the theory of Volterra. An averaging scheme is applied to this standard system, converting it to a system of differential equations which are much simpler that the initial equations. A theorem is proved which establishes the similarity of the solutions of these systems.