Differenzverfahren für Schwingungen mit trockener und zäher Reibung und für Regelungssysteme

Summary

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.