# Math Modeling and Simulation of a Chasing Game

## Location

Statesboro Campus (2054)

## Document Type and Release Option

Thesis Presentation (Open Access)

## Faculty Mentor

Dr. Yan Wu

## Faculty Mentor Email

yan@GeorgiaSouthern.edu

## Presentation Year

2022

## Start Date

16-11-2022 6:00 PM

## End Date

16-11-2022 7:00 PM

## Description

This study is based on a chasing game between two objects, one being a chaser and the other a moving target. For this problem, we assume that the chaser is always moving in a direction such that it is in line with the target. To put that assumption into a mathematical model, we used a system of differential equations to map the trajectory of the chaser. We used the fourth order Runge-Kutta method, a highly accurate method of solving ordinary differential equations, to solve these equations numerically. The goal of this project is to develop a mathematical model to precisely predict the trajectory of the chaser as it moves towards the target. We will use this model to find the minimum speed of the chaser at a specified target speed with three other fixed parameters: target path, initial dog position, and a vertical boundary. We hope to identify the impact of different system parameters on the outcome of the chasing game. This problem can be further worked on to predict minimum speeds in various chasing scenarios and could potentially be linked to the design of tactical guided missiles.

## Academic Unit

College of Science and Mathematics

Math Modeling and Simulation of a Chasing Game

Statesboro Campus (2054)

This study is based on a chasing game between two objects, one being a chaser and the other a moving target. For this problem, we assume that the chaser is always moving in a direction such that it is in line with the target. To put that assumption into a mathematical model, we used a system of differential equations to map the trajectory of the chaser. We used the fourth order Runge-Kutta method, a highly accurate method of solving ordinary differential equations, to solve these equations numerically. The goal of this project is to develop a mathematical model to precisely predict the trajectory of the chaser as it moves towards the target. We will use this model to find the minimum speed of the chaser at a specified target speed with three other fixed parameters: target path, initial dog position, and a vertical boundary. We hope to identify the impact of different system parameters on the outcome of the chasing game. This problem can be further worked on to predict minimum speeds in various chasing scenarios and could potentially be linked to the design of tactical guided missiles.