Optimization Algorithms for Projectile Motion: Maximizing Range and Determining Optimal Launch Angle

Abstract

In this paper, we undertake an in-depth exploration of the optimization of parameters governing the trajectory of a projectile. Our primary objective is the determination of the optimal launch angle and initial velocity that yield the maximum achievable range for the projectile. To accomplish this, we leverage five distinct optimization methodologies, specifically the Nelder-Mead, Powell, L-BFGS-B, TNC, and SLSQP algorithms, in pursuit of our research goals. This paper offers a comprehensive analysis of the optimization procedures, shedding light on the impact of these diverse algorithms on the resultant outcomes. For each set of optimized parameters, the manuscript conducts extensive simulations of the projectile’s trajectory, presenting visual depictions of the paths traversed by the projectile. Additionally, our study incorporates comparative charts to emphasize the performance distinctions among various algorithms with respect to both maximum range and launch angle.