Trajectory equations for a non-conservative natural system

The purpose of the article is to derive equations that determine the trajectory of a non-conservative natural system in configuration space in non-stationary external fields. A theorem on the change in the kinetic energy of the system is preliminarily proved. Lagrange equations are used to derive the equations. The derived equations can be solved numerically by the Runge-Kutta method of the 4th order. The trajectory equations together with the equality describing its parameterization form the trajectory method for solving dynamics problems.