Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Theory of Dynamical Systems with Dry Friction with Memory

Author(s):

Vladimir Semionovith Metrikin

Research Institute of mechanics of
N.I. Lobachevsky National research Nizhny Novgorod state University
603950, Nizhny Novgorod, Gagarina Avenue, 23,RIM, h.6
Associate Professor, PhD in Physics and Mathematics,

v.s.metrikin@mail.ru

Mihail Vladimirovith Zaitzev

Research Institute of mechanics of
N.I. Lobachevsky National research Nizhny Novgorod state University
postgraduate student
603950, Nizhny Novgorod. Gagarina Avenue, 23,RIM, h.6.

Nataliya Sergeevna Starodubrovskia

R.E. Alekseev Nizhni Novgorod State Technical University
assistant,PhD in Physics and Mathematics

Abstract:

In this work the dynamics of a number of frictional systems (FS) is investigated accounting for the dry friction with memory, constraints and external forces. A hybrid analytical-numerical method based on the point mapping is employed. The structure of the phase space of the FS is studied for various types of the friction, external force and position and type of the constraints. The main patterns are investigated of the evolution of the phase space trajectories associated with variation of the FS parameters. Particular attention is paid to the existence of the periodic motions of arbitrary complexity and to the transition to chaos through the period doubling bifurcation.

Keywords

• bifurcation diagram
• friction with memory
• frictional vibrations
• point mapping
• stability

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