Otimização da trajetória de um projétil em um meio com resistência do ar

Abstract

The main objective of this work is to determine the trajectory that minimizes a specific objective function, such as the flight time, the distance traveled, or the maximum height reached, subject to the constraints imposed by the physics of the problem and the initial and final conditions. Advanced optimization techniques and variational calculus will be used in this problem. The methodology includes the formulation of the optimization problem, the derivation of the Euler-Lagrange equation associated with the problem, and the development of analytical and numerical methods. Finally, the results obtained will be analyzed in terms of the optimal trajectory of the projectile, considering different launch scenarios.