Attraction for Mechanical Systems with Friction

I. A. Finogenko^a^,*

^aMatrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033 Russia

Correspondence to: *e-mail: fin@icc.ru

Received 2 July, 2021

Abstract—The asymptotic behavior of systems with Coulomb friction represented as Lagrange’s equations of the second kind is investigated. Lyapunov’s direct method is used in combination with the method of limiting equations, which goes back to the works by G.R. Sell (1967) and Z. Artstein (1977, 1978) on topological dynamics of nonautonomous systems. The results generalize LaSalle’s principle of invariance.

Keywords: Lyapunov’s functions, method of limiting equations, limiting differential inclusion, invariance principle, attraction, dry friction, Lagrange equation of the second kind

DOI: 10.1134/S1064562421050057