Further insights into the damping-induced self-recovery phenomenon
For researchers studying damping-induced self-recovery, this paper provides theoretical explanations for previously unexplained aspects of the phenomenon.
This paper addresses unanswered questions about the damping-induced self-recovery phenomenon, specifically the effects of lubricant viscosity, abrupt behavioral changes with damping, energy dynamics, and overshoots/oscillations. The authors derive an expression for the infinite-dimensional fluid-stool-wheel system, approximating its dynamics to a finite-dimensional case.
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.