TWO-DIMENSIONAL PURSUIT PROBLEMS ON PARAMETRIC CURVES

Abstract

In this paper, we provide a brief historical background on the pursuit curve problem, starting with the classical pursuit curve problem solved by
Pierre Bouguer in the 18th century. Motivated by Hathaway’s circular pursuit problem, for which no closed-form analytical solution exists, we present
a generalization based on a simple pursuit-evasion problem where the evader
moves along a parametric curve in two dimensions. Due to the difficulties or
impossibility of finding an analytical solution, we perform a numerical approximation to solve the system of differential equations that models the problem,
using the odeint function from Python. As a result, we perform computational
simulations of a two-dimensional pursuit problem to generate graphical representations of the trajectories of both the pursuer and the evader, considering
their initial positions and speeds, as well as various parametric curves for the
evader’s trajector