Euler-Lagrange Analysis of Freestanding Objects Subjected to Dynamic Excitations. Insights from the Half-Disk Model

The dynamic response of freestanding objects undergoing sliding-rolling motions under external excitations holds significant relevance across various domains of applied mechanics, among which the preservation of museum artifacts of historical and artistic value represents an important active field of research. A possible simplified geometric representation employable for pot-like artifacts is the half disk configuration. Though of a simplest archetypal nature, models like the rolling half disk bring the advantage of being exempt from ill-posedness issues which affect, for instance, rectangular rigid block models. Like canonical elementary pendulum models, the half disk model can provide insights to elucidate fundamental research issues of both theoretical and applicative significance. This contribution presents the results of computational analyses, based on the half disk model, describing the motion of pot-like mechanical systems under horizontal excitations, to investigate the influence of rolling friction ons motion stability.