Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact

R.I. Leine, N. Wouw, van de

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42 Citations (Scopus)

Abstract

Abstract In this paper, we will give conditions under which the equilibrium set of multi-degree-of-freedom non-linear mechanical systems with an arbitrary number of frictional unilateral constraints is attractive. The theorems for attractivity are proved by using the framework of measure differential inclusions together with a Lyapunov-type stability analysis and a generalisation of LaSalle’s invariance principle for non-smooth systems. The special structure of mechanical multi-body systems allows for a natural Lyapunov function and an elegant derivation of the proof. Moreover, an instability theorem for assessing the instability of equilibrium sets of non-linear mechanical systems with frictional bilateral constraints is formulated. These results are illustrated by means of examples with both unilateral and bilateral frictional constraints.
Original languageEnglish
Pages (from-to)551-583
JournalNonlinear Dynamics
Volume51
Issue number4
DOIs
Publication statusPublished - 2008

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