Comparative Analysis of Physical Correctness of Models Using Classical and Variational Integrators

This article considers the problem of modeling mechanical systems using classical integrators, such as Runge-Kutta method or explicit Euler method, associated with the decay of the main constant quantities of the system, namely momentum and energy, as well as violation of the geometric structure of the modeled system. This problem often leads to implausible and physically incorrect results. As a solution, we propose to use a variational integrator based on Lie groups. The derivation of the equations of motion for this type of integrator is described on the example of a spatial pendulum, and the results of modeling are given and compared with the results of modeling using the Runge-Kuttaa method.