COMPARATIVE ANALYSIS OF MOVING OBJECT INTERCEPTION ALGORITHMS ON PLANAR AND CURVED SURFACES USING NONLINEAR DIFFERENTIAL EQUATIONS

Abstract

This paper presents a comparative analysis of interception algorithms for moving objects on planar and curved surfaces using nonlinear differential equations. The study investigates how geometric properties of the underlying surface influence interception time, trajectory curvature, and overall system stability. A nonlinear pursuit model is formulated for both planar and curved manifolds, and numerical simulations are conducted to evaluate the performance of different interception strategies. Comparative results demonstrate that curvature significantly affects the dynamics of pursuit, leading to measurable differences in optimal interception paths and convergence behavior. The findings provide valuable insights for applications in robotics, autonomous navigation, aerospace systems, and mathematical modeling of dynamic interactions on complex geometries