Mathematics – Classical Analysis and ODEs
Scientific paper
2008-10-27
Mathematics
Classical Analysis and ODEs
12 pages, 2 figures, preprint of the Invited paper for Collections of papers to the memory of V.V. Rumyancev, Russian Academy
Scientific paper
In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity hyperplanes transversally and that the system is smooth outside of these hyperplanes. Such a situation is natural for mechanical systems with dry friction and without constraints and sticking of oscillations. To illustrate the result we prove stability of the velocity of vibration-induced displacement.
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