2024/11/04 by Nick Lorenzo, Lorenzo, Nick
Engineering · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Guidance and Control Systems #Military Defense Systems Analysis #Sports Dynamics and Biomechanics
paper · pdf · doi:10.48550/arxiv.2411.02145
openalex publication_date 2024/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to O ( ε ), for the position and velocity of the projectile, where ε is a small perturbation parameter; in the special case of constant wind, we provide closed-form solutions, exact to O ( ε ). Under the constant-wind assumption, we provide closed-form solutions of O ( 1 ) for the time of tangency, times of flight, and extreme values of the radius achieved by the projectile. We provide physical interpretations throughout, including a physical interpretation of the branches W0 and W -1 of the Lambert W function in the context of flight time. We also provide parameterized, error-controlled algorithms to compute trajectories, complete with a full Matlab implementation that we make freely available. We compare the results of our implementation to a general-purpose, stiff ODE solver.