Periodic motions generated from non-autonomous grazing dynamics

TL;DR

This paper investigates the existence and stability of grazing periodic solutions in non-autonomous impulsive systems with stationary impact conditions, providing new linearization methods and mechanical examples.

Contribution

It introduces a novel approach to analyze non-autonomous impulsive systems with time-independent impact conditions, including new linearization techniques and stability criteria.

Findings

Established conditions for existence of grazing periodic solutions

Derived stability criteria under regular perturbations

Validated results with mechanical system examples

Abstract

This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are stationary, and this makes necessity to study the problem in a new way. The models play exceptionally important role in mechanics and electronics. A concise review on the sufficient conditions for the new type of linearization is presented. The existence and stability of periodic solutions are considered under the circumstance of the regular perturbation. To visualize the theoretical results, mechanical examples are presented.