Solution for projectile motion in two dimensions with nonlinear air resistance using Laplace decomposition method

Abstract

Laplace decomposition method (LDM) is utilized to obtain an approximate solution of two-dimensional projectile motion with linear air resistance as well as to derive a formalism to obtain the solutions for any order of nonlinearity in the air resistance. The projectile trajectory was obtained using LDM method in three cases: without air resistance, with linear air resistance, and with quadratic air resistance. The solutions were used to illustrate the effect of the order of non-linearity on the basic parameters related to the motion, like Ranges, time of flight, maximum high and some other parameters. The available literature does not provide an exact solution to this motion when higher nonlinearities are involved. Nevertheless, the results show that such method is effective and powerful in getting approximate solutions for problems involving nonlinear behavior.