Trajectory equations for a non-conservative natural system

TL;DR

This paper derives trajectory equations for non-conservative natural systems in external fields using Lagrange equations, providing a basis for numerical solutions via Runge-Kutta methods to analyze system dynamics.

Contribution

It introduces a new set of trajectory equations for non-conservative systems in external fields, expanding the analytical tools for such dynamics problems.

Findings

Derived equations can be solved numerically with Runge-Kutta 4th order method

Established a theorem on kinetic energy change in the system

Presented a trajectory method for solving dynamics problems

Abstract

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.