Investigating the classical problem of pursuit, in two modes

TL;DR

This paper explores pursuit problems involving multiple moving agents on lines and curves, introducing new relationships and analyzing natural pursuit behaviors like moths around lamps.

Contribution

It introduces novel relationships for two- and N-particle pursuit systems and extends classical pursuit analysis to curved movements and biological examples.

Findings

New pursuit relationships for multi-particle systems

Comparison of pursuit methods on straight lines

Analysis of moths' pursuit behavior around lamps

Abstract

The pursuit problem is a historical issue of the application of mathematics in physics, which has been discussed for centuries since the time of Leonardo Da Vinci, and its applications are wide ranging from military and industrial to recreational, but its place of interest is nowhere but nature and inspiration from the way of migration of birds and hunting of archer fish. The pursuit problem involves one or more pursuers trying to catch a target that is moving in a certain direction. In this article, we delve into two modes of movement: movement on a straight line and movement on a curve. Our primary focus is on the latter. Within the context of movement on a straight line, we explore two methods and compare their respective results. Furthermore, we investigate the movement of two particles chasing each other and extend these findings to N particles that are chasing each other in pairs. By leveraging these two modes of movement, we present a novel relationship for two-particle and N-particle systems in pursuit. Lastly, we analyze the movement of moths around a lamp and evaluate their motion in relation to two-particle and N-particle systems in pursuit. The results of this analysis are carefully examined.