Motion of a system of oscillators under the generalized dry friction control

TL;DR

This paper investigates the existence and uniqueness of motion in a system of linear oscillators controlled by a generalized dry-friction mechanism, using advanced mathematical theories to address the problem.

Contribution

It introduces a novel approach to analyze the control of oscillators with dry-friction type control through the DiPerna--Lions theory.

Findings

Existence of motion is established under generalized dry-friction control.

Uniqueness of solutions is proven within the framework of singular differential equations.

The approach applies to systems with arbitrary numbers of oscillators.

Abstract

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to equilibrium. The problem of existence and uniqueness of motion under the suggested control is resolved within the framework of the DiPerna--Lions theory of singular ordinary differential equations.