Homotopy-Analysis-Method-Based Solutions of Quintic Nonlinear Angular Motion for Projectiles

摘要

The current research literature has shown that the nonlinear aerodynamic coefficients have a significant impact on the angular motion of projectiles. However, high-order aerodynamic coefficients, such as quintic terms, are seldom considered due to their complexity and the lack of an appropriate analytical workhorse. The homotopy analysis method is becoming a popular analytical tool for nonlinear problems because it can address strong nonlinearities without relying on any small or large physical parameters. An efficient approach to determine the convergence-control parameter is proposed and incorporated into the basic algorithm of the homotopy analysis method. This new algorithm is applied to two problems from the ballistics community literature to which quintic static moments are deliberately added and analytical solutions in general forms are obtained. By presenting some numerical examples, it is demonstrated that this algorithm is highly efficient and accurate over a wide region of convergence. As a result, the effects of the nonlinear aerodynamic parameters and initial angle of attack on the property of angular motion are well described mathematically using these formulas. The results of this research provide a reference for studying more complicated problems related to nonlinear projectile motion.