Чисельне моделювання динаміки руху тіла у тривимірному просторі методом Рунге-Кутти

Abstract

The paper considers the actual problem of numerical modeling of material point dynamics in three-dimensional space. The features of software implementation of the fourth-order Runge-Kutta method for a system of differential equations describing the object state via a six-component vector are analyzed. A comparative analysis of the algorithm's efficiency against Euler's method is conducted using the example of ballistic motion simulation considering nonlinear aerodynamic drag. The research results confirm the high accuracy and energy stability of the RK4 method in reproducing complex spatial trajectories, which allows recommending it for use in modern physics engines and robotics systems.