Features of gap estimation in model problem of flipping particle with unilateral con-straints

The article presents the research results of mechanical systems with unilateral constraints. The model problem of flipping a particle on a horizontal surface with unilateral constraints under gravitation is considered. The re-search deals with the time and height of the particle reaching the surface in accordance with the surface frequency and vibration amplitude. The estimation of the gap between the material particle and the vibration surface is obtained. The paper presents analytical ratios of frequency and the surface vibration amplitude that provide a predetermined height or the reaching time of the material particle. A number of maximum flipping characteristics are given. The paper discusses restrictions on the mathematical model parameters, based on the surface physical characteristics and the ways to modify the original mathematical model. The methodological framework can be used in the research of continuous flipping mode, taking into consideration some additional constant force.