Differenzverfahren f�r Schwingungen mit trockener und z�her Reibung und f�r Regelungssysteme

Abstract

In the present article we show that the solutions of initial value problems in ordinary differential equations with discontinuous right-hand side can be approximated by a slight modification of the Euler-Cauchy method. The method is succesfully applied to $$\ddot x + 2D\dot x + \mu sgn(\dot x) + cx = \alpha \cos (\Omega t)$$ and $$\ddot x + 2D\omega x + \omega ^2 x = - sgn(x + \dot x)$$ for some initial values. By a solution of a differential equation with discontinuous right-hand side we mean the concept given by A. F. Filippov.