Projectile motion under quadratic air resistence via multistep-differential transformation method

Abstract

The projectile motion system was examined in this study when air resistance was present (we only looked at the situation of quadratic air resistance). First, we used Newtonian mechanics to derive the equation governing the system. Second, the study focused on the projectile motion’s characteristics, namely its maximum height and maximum horizontal range. Additionally, we used simulation plots to apply the Differential Transform Method (DTM) and the Multistep Differential Transform Method (Ms-DTM) to solve the equations found. This allowed us to discuss the projectile’s trajectory. We computed the flying time and the maximum range by comparing our findings with experimental data from published research. In the end, the absolute errors were computed to find the optimal numerical approach to solve this problem.