Mathematical formulation of a dynamical system with dry friction subjected to external forces

A new test for stick-slip limit cycles in dry-friction oscillators with small nonlinear friction characteristics

We consider a dry friction oscillator on a moving belt with both the Coulomb friction and a small nonlinear addition which can model e.g. the Stribeck effect. By using the perturbation theory, we establish a new sufficient condition for the nonlinearity to ensure the occurrence of a stick-slip limit cycle. The test obtained is more accurate compared to what one gets by building upon the divergence test.

振动冲击能量采集器中的干摩擦动力学分析

Analysis of Dry Friction Dynamics in a Vibro-Impact Energy Harvester

本文研究含干摩擦的倾斜胶囊-子弹式振动冲击能量采集器，通过解析条件与非线性映射分析滑动、冲击及分岔转变，揭示干摩擦对能量输出的复杂影响。

One-dimensional chaos in a system with dry friction: analytical approach

We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding mathematical model is represented. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (a base map). For this base map we demonstrate there is a domain of parameters where a robust chaotic dynamics can be observed. Namely, we prove existence of an infinite set of periodic points of arbitrarily big period. Mo…

On motions without falling of an inverted pendulum with dry friction

An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the presence of dry friction. Sufficient conditions for the existence of solutions along which the pendulum never falls below the horizontal positions are presented. The proof is based on the fact that solutions of the corresponding differential inclusion are right-unique and continuously depend on initial conditions, which is also shown in the paper.

Damping of a system of linear oscillators using the generalized dry friction

The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with discontinuous right-hand side. A uniqueness and continuity theorem is proved for the phase flow of this system. Thus, the control in the form of generalized dry friction defines the motion of the system of oscillators uniquely.

On generalized Coulomb-Amontons' law in the context of rigid body dynamics

A generalization of Coulomb-Amontons' law of dry friction recently proposed by V. V. Kozlov is considered in the context of rigid body dynamics. Universal requirements for dry friction tensor formulated by V. V. Kozlov are complemented by a condition taking into account the contact nature of dry friction and applied to several models. For the famous Painleve problem a generalized Coulomb-Amontons' force without singularities, yet such that the dissipation takes place only at the point of contact, is found. By the example of the motion of a rigid ball on a plane with a single point of contact, …