Further insights into the damping-induced self-recovery phenomenon

TL;DR

This paper provides theoretical insights into the damping-induced self-recovery phenomenon, addressing key questions about fluid effects, energy dynamics, and oscillations through derived mathematical models.

Contribution

It introduces a theoretical framework that approximates the complex fluid-structure system, explaining observed behaviors and effects of damping and control laws.

Findings

Derived an expression for the fluid-stool-wheel system dynamics.

Explained the impact of lubricant viscosity on recovery.

Analyzed the energy flow and oscillation phenomena.

Abstract

In a series of papers, D. E. Chang, et al., proved and experimentally demonstrated a phenomenon they termed "damping-induced self-recovery". However, these papers left a few questions concerning the observed phenomenon unanswered - in particular, the effect of the intervening lubricant-fluid and its viscosity on the recovery, the abrupt change in behaviour with the introduction of damping, a description of the energy dynamics, and the curious occurrence of overshoots and oscillations and its dependence on the control law. In this paper we attempt to answer these questions through theory. In particular, we derive an expression for the infinite-dimensional fluid-stool-wheel system, that approximates its dynamics to that of the better understood finite-dimensional case.