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

TL;DR

This paper addresses damping of linear oscillators using a control modeled as generalized dry friction, proving the system's motion is uniquely determined despite the discontinuous control.

Contribution

It introduces a control approach with generalized dry friction for damping oscillators and proves the uniqueness and continuity of the resulting system motion.

Findings

Control in the form of dry friction ensures unique system motion.

The system's differential equations with discontinuous right-hand side are well-posed.

The phase flow of the system is proven to be continuous and unique.

Abstract

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.