A Numerical Procedure for the Determination of the Pursuit Curve of Objects with Uniformly Accelerated Motion

TL;DR

This paper develops a numerical method to determine pursuit curves for objects with various accelerations and initial speeds, extending classical pursuit problem solutions to more complex motion scenarios.

Contribution

It introduces a numerical procedure for calculating pursuit curves when the target moves along arbitrary paths, generalizing previous solutions for simpler motion cases.

Findings

Derived conditions where pursuit curves match uniform motion cases.

Provided a numerical method for arbitrary target trajectories.

Extended pursuit problem solutions to objects with different accelerations.

Abstract

In this article the pursuit problem of objects that moves with different accelerations and initial speeds is studied. Initially, the situation in which the escaping object moves in a straight line is considered. Under this condition, and if both objects starts from rest, it is shown that the trajectory of the chasing object match those obtain for the case of uniform motions. When both objects have different initial speeds and accelerations, we first note that if the escaping object starts its motion with a speed which is function of the acceleration and initial speed of the chasing object, then the pursuit curve is the same obtained for no initial speeds. Latter solution is used to solve the chase problem when both objects have different accelerations and initial speeds. Finally, making use of the preceding results, a numerical procedure is proposed for obtaining the pursuit curve when the escaping object moves in an arbitrary path.