用平均方法得到的不连续系统非粘着周期振荡的稳定性。I.不连续曲面系统的外光滑
Stability of non-sticking periodic oscillations obtained via the averaging method in discontinuous systems. I. Smooth outside of the discontinuity surfaces systems
摘要：
本文证明了关于小参数光滑系统周期解的Bogolyubov第二定理在不连续系统中的成立。假设生成解与不连续超平面横向相交，并且系统在这些超平面之外是光滑的。这种情况对于具有干摩擦并且没有约束和振荡的粘滞的机械系统是自然的。为了说明这一结果，我们证明了振动诱导位移速度的稳定性。
英文摘要：
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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