Zero Time Discontinuity Mapping (ZDM) and Poincar\'e Discontinuity Mapping (PDM) in a neighbourhood of a regular grazing point of order 4 in impacting hybrid systems

TL;DR

This paper introduces ZDM and PDM methods to accurately analyze impact hybrid systems near a regular grazing point of order 4, improving the understanding of their local dynamics.

Contribution

The paper develops ZDM and PDM techniques specifically for neighborhoods of order 4 grazing points in impacting hybrid systems, enhancing local flow analysis.

Findings

ZDM and PDM effectively correct flow behavior near grazing points.

Application of methods improves understanding of impact system dynamics.

Methods are tailored for regular grazing points of order 4.

Abstract

In this work, we study the dynamics of an impact hybrid system. We built applications called ZDM (Zero Discontinuity Mapping) and PDM (Poincar\'e Discontinuity Mapping), for points in a neighbourhood of the 4 order regular grazing point, whose objective is to correct the behaviour of flows in the neighbourhood of this points.